Solve 5(2x-10)-y(5y-6)=1

$$5(2x-10)-y(5y-6)=1$$

Solve for x

$$x=\frac{y^{2}}{2}-\frac{3y}{5}+\frac{51}{10}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 2x-10.

$$10x-50-y\left(5y-6\right)=1$$

Use the distributive property to multiply y by 5y-6.

$$10x-50-\left(5y^{2}-6y\right)=1$$

To find the opposite of 5y^{2}-6y, find the opposite of each term.

$$10x-50-5y^{2}+6y=1$$

Add 50 to both sides.

$$10x-5y^{2}+6y=1+50$$

Add 1 and 50 to get 51.

$$10x-5y^{2}+6y=51$$

Add 5y^{2} to both sides.

$$10x+6y=51+5y^{2}$$

Subtract 6y from both sides.

$$10x=51+5y^{2}-6y$$

The equation is in standard form.

$$10x=5y^{2}-6y+51$$

Divide both sides by 10.

$$\frac{10x}{10}=\frac{5y^{2}-6y+51}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$x=\frac{5y^{2}-6y+51}{10}$$

Divide 51+5y^{2}-6y by 10.

$$x=\frac{y^{2}}{2}-\frac{3y}{5}+\frac{51}{10}$$

Solve for y (complex solution)

$$y=\frac{-\sqrt{50x-246}+3}{5}$$

$$y=\frac{\sqrt{50x-246}+3}{5}$$

Solve for y

$$y=\frac{-\sqrt{50x-246}+3}{5}$$

$$y=\frac{\sqrt{50x-246}+3}{5}\text{, }x\geq \frac{123}{25}$$