Solve Deltac^2-2sqrt{6}x+5=0

$$\Delta c ^ { 2 } - 2 \sqrt { 6 } x + 5 = 0$$

Solve for x

$$x=\frac{\sqrt{6}\left(\Delta c^{2}+5\right)}{12}$$

Steps for Solving Linear Equation

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$\Delta c^{2}-2\sqrt{6}x=-5$$

Subtract \Delta c^{2} from both sides.

$$-2\sqrt{6}x=-5-\Delta c^{2}$$

The equation is in standard form.

$$\left(-2\sqrt{6}\right)x=-\Delta c^{2}-5$$

Divide both sides by -2\sqrt{6}.

$$\frac{\left(-2\sqrt{6}\right)x}{-2\sqrt{6}}=\frac{-\Delta c^{2}-5}{-2\sqrt{6}}$$

Dividing by -2\sqrt{6} undoes the multiplication by -2\sqrt{6}.

$$x=\frac{-\Delta c^{2}-5}{-2\sqrt{6}}$$

Divide -5-\Delta c^{2} by -2\sqrt{6}.

$$x=\frac{\sqrt{6}\left(\Delta c^{2}+5\right)}{12}$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=-i\Delta ^{-\frac{1}{2}}\sqrt{-2\sqrt{6}x+5}\text{; }c=i\Delta ^{-\frac{1}{2}}\sqrt{-2\sqrt{6}x+5}\text{, }&\Delta \neq 0\\c\in \mathrm{C}\text{, }&x=\frac{5\sqrt{6}}{12}\text{ and }\Delta =0\end{matrix}\right.$$

Solve for c

$$\left\{\begin{matrix}c=\sqrt{\frac{2\sqrt{6}x-5}{\Delta }}\text{; }c=-\sqrt{\frac{2\sqrt{6}x-5}{\Delta }}\text{, }&\left(\Delta >0\text{ or }x\leq \frac{5\sqrt{6}}{12}\right)\text{ and }\left(\Delta <0\text{ or }x\geq \frac{5\sqrt{6}}{12}\right)\text{ and }\Delta \neq 0\\c\in \mathrm{R}\text{, }&x=\frac{5\sqrt{6}}{12}\text{ and }\Delta =0\end{matrix}\right.$$