-4y(3y+8)=3

Solution for -4y(3y+8)=3 equation:

-4y(3y+8)=3

We move all terms to the left:

-4y(3y+8)-(3)=0

We multiply parentheses

-12y^2-32y-3=0

a = -12; b = -32; c = -3;
Δ = b2-4ac
Δ = -322-4·(-12)·(-3)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{55}}{2*-12}=\frac{32-4\sqrt{55}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{55}}{2*-12}=\frac{32+4\sqrt{55}}{-24}
$