Solve y=9x^2-12x+35a

$$y = 9 x ^ { 2 } - 12 x + 35 a$$

Solve for a

$$a=\frac{y+12x-9x^{2}}{35}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$9x^{2}-12x+35a=y$$

Subtract 9x^{2} from both sides.

$$-12x+35a=y-9x^{2}$$

Add 12x to both sides.

$$35a=y-9x^{2}+12x$$

The equation is in standard form.

$$35a=y+12x-9x^{2}$$

Divide both sides by 35.

$$\frac{35a}{35}=\frac{y+12x-9x^{2}}{35}$$

Dividing by 35 undoes the multiplication by 35.

$$a=\frac{y+12x-9x^{2}}{35}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y-35a+4}+2}{3}$$

$$x=\frac{-\sqrt{y-35a+4}+2}{3}$$

Solve for x

$$x=\frac{\sqrt{y-35a+4}+2}{3}$$

$$x=\frac{-\sqrt{y-35a+4}+2}{3}\text{, }y\geq 35a-4$$