(3y+17)(3y-29)=180

Solution for (3y+17)(3y-29)=180 equation:

(3y+17)(3y-29)=180

We move all terms to the left:

(3y+17)(3y-29)-(180)=0

We multiply parentheses ..

(+9y^2-87y+51y-493)-180=0

We get rid of parentheses

9y^2-87y+51y-493-180=0

We add all the numbers together, and all the variables

9y^2-36y-673=0

a = 9; b = -36; c = -673;
Δ = b2-4ac
Δ = -362-4·9·(-673)
Δ = 25524
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:

$\sqrt{\Delta}=\sqrt{25524}=\sqrt{36*709}=\sqrt{36}*\sqrt{709}=6\sqrt{709}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{709}}{2*9}=\frac{36-6\sqrt{709}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{709}}{2*9}=\frac{36+6\sqrt{709}}{18}
$