Solve 5y^2+2x-21y+20=0

$$5 y ^ { 2 } + 2 x - 21 y + 20 = 0$$

Solve for x

$$x=-\frac{5y^{2}}{2}+\frac{21y}{2}-10$$

Steps for Solving Linear Equation

Subtract 5y^{2} from both sides. Anything subtracted from zero gives its negation.

$$2x-21y+20=-5y^{2}$$

Add 21y to both sides.

$$2x+20=-5y^{2}+21y$$

Subtract 20 from both sides.

$$2x=-5y^{2}+21y-20$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{-5y^{2}+21y-20}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{-5y^{2}+21y-20}{2}$$

Divide -5y^{2}+21y-20 by 2.

$$x=-\frac{5y^{2}}{2}+\frac{21y}{2}-10$$

Solve for y (complex solution)

$$y=\frac{\sqrt{41-40x}+21}{10}$$

$$y=\frac{-\sqrt{41-40x}+21}{10}$$

Solve for y

$$y=\frac{\sqrt{41-40x}+21}{10}$$

$$y=\frac{-\sqrt{41-40x}+21}{10}\text{, }x\leq \frac{41}{40}$$