Solve sqrt{2}quadO^2-sqrt{6}C+1=0

$$\sqrt { 2 } \quad O ^ { 2 } - \sqrt { 6 } C + 1 = 0$$

Solve for C

$$C=\frac{\sqrt{6}\left(\sqrt{2}O^{2}+1\right)}{6}$$

Steps for Solving Linear Equation

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{2}O^{2}-\sqrt{6}C=-1$$

Subtract \sqrt{2}O^{2} from both sides.

$$-\sqrt{6}C=-1-\sqrt{2}O^{2}$$

The equation is in standard form.

$$\left(-\sqrt{6}\right)C=-\sqrt{2}O^{2}-1$$

Divide both sides by -\sqrt{6}.

$$\frac{\left(-\sqrt{6}\right)C}{-\sqrt{6}}=\frac{-\sqrt{2}O^{2}-1}{-\sqrt{6}}$$

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

$$C=\frac{-\sqrt{2}O^{2}-1}{-\sqrt{6}}$$

Divide -1-\sqrt{2}O^{2} by -\sqrt{6}.

$$C=\frac{\sqrt{3}O^{2}}{3}+\frac{\sqrt{6}}{6}$$

Solve for O

$$O=\frac{2^{\frac{3}{4}}\sqrt{\sqrt{6}C-1}}{2}$$

$$O=-\frac{2^{\frac{3}{4}}\sqrt{\sqrt{6}C-1}}{2}\text{, }C\geq \frac{\sqrt{6}}{6}$$