4y-2y(y-8)=13

Solution for 4y-2y(y-8)=13 equation:

4y-2y(y-8)=13

We move all terms to the left:

4y-2y(y-8)-(13)=0

We multiply parentheses

-2y^2+4y+16y-13=0

We add all the numbers together, and all the variables

-2y^2+20y-13=0

a = -2; b = 20; c = -13;
Δ = b2-4ac
Δ = 202-4·(-2)·(-13)
Δ = 296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{74}}{2*-2}=\frac{-20-2\sqrt{74}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{74}}{2*-2}=\frac{-20+2\sqrt{74}}{-4}
$