Solve 3y^2-24y-x+45=0

$$3 y ^ { 2 } - 24 y - x + 45 = 0$$

Solve for x

$$x=3\left(y-5\right)\left(y-3\right)$$

Steps for Solving Linear Equation

Subtract 3y^{2} from both sides. Anything subtracted from zero gives its negation.

$$-24y-x+45=-3y^{2}$$

Add 24y to both sides.

$$-x+45=-3y^{2}+24y$$

Subtract 45 from both sides.

$$-x=-3y^{2}+24y-45$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{3\left(3-y\right)\left(y-5\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{3\left(3-y\right)\left(y-5\right)}{-1}$$

Divide 3\left(-5+y\right)\left(3-y\right) by -1.

$$x=-3\left(3-y\right)\left(y-5\right)$$

Solve for y (complex solution)

$$y=\frac{\sqrt{3x+9}}{3}+4$$

$$y=-\frac{\sqrt{3x+9}}{3}+4$$

Solve for y

$$y=\frac{\sqrt{3x+9}}{3}+4$$

$$y=-\frac{\sqrt{3x+9}}{3}+4\text{, }x\geq -3$$