-4y(3y-2)=-11

Solution for -4y(3y-2)=-11 equation:

-4y(3y-2)=-11

We move all terms to the left:

-4y(3y-2)-(-11)=0

We add all the numbers together, and all the variables

-4y(3y-2)+11=0

We multiply parentheses

-12y^2+8y+11=0

a = -12; b = 8; c = +11;
Δ = b2-4ac
Δ = 82-4·(-12)·11
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{37}}{2*-12}=\frac{-8-4\sqrt{37}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{37}}{2*-12}=\frac{-8+4\sqrt{37}}{-24}
$