-4y(5y+6)=-7y+2

Solution for -4y(5y+6)=-7y+2 equation:

-4y(5y+6)=-7y+2

We move all terms to the left:

-4y(5y+6)-(-7y+2)=0

We multiply parentheses

-20y^2-24y-(-7y+2)=0

We get rid of parentheses

-20y^2-24y+7y-2=0

We add all the numbers together, and all the variables

-20y^2-17y-2=0

a = -20; b = -17; c = -2;
Δ = b2-4ac
Δ = -172-4·(-20)·(-2)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{129}}{2*-20}=\frac{17-\sqrt{129}}{-40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{129}}{2*-20}=\frac{17+\sqrt{129}}{-40}
$