Solve 17a^2-78x-8=0

$$17 a ^ { 2 } - 78 x - 8 = 0$$

Solve for x

$$x=\frac{17a^{2}}{78}-\frac{4}{39}$$

Steps for Solving Linear Equation

Subtract 17a^{2} from both sides. Anything subtracted from zero gives its negation.

$$-78x-8=-17a^{2}$$

Add 8 to both sides.

$$-78x=-17a^{2}+8$$

The equation is in standard form.

$$-78x=8-17a^{2}$$

Divide both sides by -78.

$$\frac{-78x}{-78}=\frac{8-17a^{2}}{-78}$$

Dividing by -78 undoes the multiplication by -78.

$$x=\frac{8-17a^{2}}{-78}$$

Divide -17a^{2}+8 by -78.

$$x=\frac{17a^{2}}{78}-\frac{4}{39}$$

Solve for a (complex solution)

$$a=-\frac{\sqrt{1326x+136}}{17}$$

$$a=\frac{\sqrt{1326x+136}}{17}$$

Solve for a

$$a=\frac{\sqrt{1326x+136}}{17}$$

$$a=-\frac{\sqrt{1326x+136}}{17}\text{, }x\geq -\frac{4}{39}$$