2y(2-2y)-5y=3y-20

Solution for 2y(2-2y)-5y=3y-20 equation:

2y(2-2y)-5y=3y-20

We move all terms to the left:

2y(2-2y)-5y-(3y-20)=0

We add all the numbers together, and all the variables

2y(-2y+2)-5y-(3y-20)=0

We add all the numbers together, and all the variables

-5y+2y(-2y+2)-(3y-20)=0

We multiply parentheses

-4y^2-5y+4y-(3y-20)=0

We get rid of parentheses

-4y^2-5y+4y-3y+20=0

We add all the numbers together, and all the variables

-4y^2-4y+20=0

a = -4; b = -4; c = +20;
Δ = b2-4ac
Δ = -42-4·(-4)·20
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{21}}{2*-4}=\frac{4-4\sqrt{21}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{21}}{2*-4}=\frac{4+4\sqrt{21}}{-8}
$