(2y-40)(8y-40)=-576

Solution for (2y-40)(8y-40)=-576 equation:

(2y-40)(8y-40)=-576

We move all terms to the left:

(2y-40)(8y-40)-(-576)=0

We add all the numbers together, and all the variables

(2y-40)(8y-40)+576=0

We multiply parentheses ..

(+16y^2-80y-320y+1600)+576=0

We get rid of parentheses

16y^2-80y-320y+1600+576=0

We add all the numbers together, and all the variables

16y^2-400y+2176=0

a = 16; b = -400; c = +2176;
Δ = b2-4ac
Δ = -4002-4·16·2176
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-144}{2*16}=\frac{256}{32}
=8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+144}{2*16}=\frac{544}{32}
=17
$