\[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]

\[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]

\[\begin{cases} \frac{2 \cdot c}{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]

\[\color{red}{\begin{cases} \frac{2 \cdot c}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{c}{\frac{c}{b} \cdot a - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}}\]

\[\begin{cases} \color{red}{\frac{c}{\frac{c}{b} \cdot a - b}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \color{blue}{\frac{1}{\frac{\frac{c}{b} \cdot a - b}{c}}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]

\[\begin{cases} \frac{1}{\color{red}{\frac{\frac{c}{b} \cdot a - b}{c}}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{1}{\color{blue}{\frac{a}{b} - \frac{b}{c}}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]

\[\begin{cases} \frac{1}{\color{red}{\frac{a}{b} - \frac{b}{c}}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{1}{\color{blue}{e^{\log \left(\frac{a}{b} - \frac{b}{c}\right)}}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]

\[\begin{cases} \color{red}{\frac{1}{e^{\log \left(\frac{a}{b} - \frac{b}{c}\right)}}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \color{blue}{e^{-\log \left(\frac{a}{b} - \frac{b}{c}\right)}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]

\[\begin{cases} e^{-\log \left(\frac{a}{b} - \frac{b}{c}\right)} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} e^{-\left(\left(\log -1 + \log b\right) - \log c\right)} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]

\[\begin{cases} e^{-\color{red}{\left(\left(\log -1 + \log b\right) - \log c\right)}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} e^{-\color{blue}{\left(\left(\log -1 + \log b\right) - \log c\right)}} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]

\[\begin{cases} e^{-\left(\left(\log -1 + \log b\right) - \log c\right)} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{1}{e^{\log b} \cdot -1} \cdot c & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]

\[\color{red}{\begin{cases} \frac{1}{e^{\log b} \cdot -1} \cdot c & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{c}{-b} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - c \cdot \left(a \cdot 4\right)}}{a \cdot 2} & \text{otherwise} \end{cases}}\]