(3y+5)(9y-11)=180

Solution for (3y+5)(9y-11)=180 equation:

(3y+5)(9y-11)=180

We move all terms to the left:

(3y+5)(9y-11)-(180)=0

We multiply parentheses ..

(+27y^2-33y+45y-55)-180=0

We get rid of parentheses

27y^2-33y+45y-55-180=0

We add all the numbers together, and all the variables

27y^2+12y-235=0

a = 27; b = 12; c = -235;
Δ = b2-4ac
Δ = 122-4·27·(-235)
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{-(12)-6\sqrt{709}}{2*27}=\frac{-12-6\sqrt{709}}{54}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{709}}{2*27}=\frac{-12+6\sqrt{709}}{54}
$