(3y+7)(9y+5)=180

Solution for (3y+7)(9y+5)=180 equation:

(3y+7)(9y+5)=180

We move all terms to the left:

(3y+7)(9y+5)-(180)=0

We multiply parentheses ..

(+27y^2+15y+63y+35)-180=0

We get rid of parentheses

27y^2+15y+63y+35-180=0

We add all the numbers together, and all the variables

27y^2+78y-145=0

a = 27; b = 78; c = -145;
Δ = b2-4ac
Δ = 782-4·27·(-145)
Δ = 21744
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:

$\sqrt{\Delta}=\sqrt{21744}=\sqrt{144*151}=\sqrt{144}*\sqrt{151}=12\sqrt{151}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-12\sqrt{151}}{2*27}=\frac{-78-12\sqrt{151}}{54}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+12\sqrt{151}}{2*27}=\frac{-78+12\sqrt{151}}{54}
$