(3y-2)(2y+4)=180

Solution for (3y-2)(2y+4)=180 equation:

(3y-2)(2y+4)=180

We move all terms to the left:

(3y-2)(2y+4)-(180)=0

We multiply parentheses ..

(+6y^2+12y-4y-8)-180=0

We get rid of parentheses

6y^2+12y-4y-8-180=0

We add all the numbers together, and all the variables

6y^2+8y-188=0

a = 6; b = 8; c = -188;
Δ = b2-4ac
Δ = 82-4·6·(-188)
Δ = 4576
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:

$\sqrt{\Delta}=\sqrt{4576}=\sqrt{16*286}=\sqrt{16}*\sqrt{286}=4\sqrt{286}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{286}}{2*6}=\frac{-8-4\sqrt{286}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{286}}{2*6}=\frac{-8+4\sqrt{286}}{12}
$