-4(-5y+1)-2y=2y(y-5)-6

Solution for -4(-5y+1)-2y=2y(y-5)-6 equation:

-4(-5y+1)-2y=2y(y-5)-6

We move all terms to the left:

-4(-5y+1)-2y-(2y(y-5)-6)=0

We add all the numbers together, and all the variables

-2y-4(-5y+1)-(2y(y-5)-6)=0

We multiply parentheses

-2y+20y-(2y(y-5)-6)-4=0


We calculate terms in parentheses: -(2y(y-5)-6), so:

2y(y-5)-6

We multiply parentheses

2y^2-10y-6

Back to the equation:

-(2y^2-10y-6)


We add all the numbers together, and all the variables

18y-(2y^2-10y-6)-4=0

We get rid of parentheses

-2y^2+18y+10y+6-4=0

We add all the numbers together, and all the variables

-2y^2+28y+2=0

a = -2; b = 28; c = +2;
Δ = b2-4ac
Δ = 282-4·(-2)·2
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-20\sqrt{2}}{2*-2}=\frac{-28-20\sqrt{2}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+20\sqrt{2}}{2*-2}=\frac{-28+20\sqrt{2}}{-4}
$