Solve (8-y)^2-5^2=(4-y)^2+3^2

$$( 8 - y ) ^ { 2 } - 5 ^ { 2 } = ( 4 - y ) ^ { 2 } + 3 ^ { 2 }$$

Solve for y

$$y = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-y\right)^{2}.

$$64-16y+y^{2}-5^{2}=\left(4-y\right)^{2}+3^{2}$$

Calculate 5 to the power of 2 and get 25.

$$64-16y+y^{2}-25=\left(4-y\right)^{2}+3^{2}$$

Subtract 25 from 64 to get 39.

$$39-16y+y^{2}=\left(4-y\right)^{2}+3^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4-y\right)^{2}.

$$39-16y+y^{2}=16-8y+y^{2}+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$39-16y+y^{2}=16-8y+y^{2}+9$$

Add 16 and 9 to get 25.

$$39-16y+y^{2}=25-8y+y^{2}$$

Add 8y to both sides.

$$39-16y+y^{2}+8y=25+y^{2}$$

Combine -16y and 8y to get -8y.

$$39-8y+y^{2}=25+y^{2}$$

Subtract y^{2} from both sides.

$$39-8y+y^{2}-y^{2}=25$$

Combine y^{2} and -y^{2} to get 0.

$$39-8y=25$$

Subtract 39 from both sides.

$$-8y=25-39$$

Subtract 39 from 25 to get -14.

$$-8y=-14$$

Divide both sides by -8.

$$y=\frac{-14}{-8}$$

Reduce the fraction \frac{-14}{-8} to lowest terms by extracting and canceling out -2.

$$y=\frac{7}{4}$$