(3x+3)(5x+1)=180

Solution for (3x+3)(5x+1)=180 equation:

(3x+3)(5x+1)=180

We move all terms to the left:

(3x+3)(5x+1)-(180)=0

We multiply parentheses ..

(+15x^2+3x+15x+3)-180=0

We get rid of parentheses

15x^2+3x+15x+3-180=0

We add all the numbers together, and all the variables

15x^2+18x-177=0

a = 15; b = 18; c = -177;
Δ = b2-4ac
Δ = 182-4·15·(-177)
Δ = 10944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10944}=\sqrt{576*19}=\sqrt{576}*\sqrt{19}=24\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-24\sqrt{19}}{2*15}=\frac{-18-24\sqrt{19}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+24\sqrt{19}}{2*15}=\frac{-18+24\sqrt{19}}{30}
$