(3x+3)(5x-2)=180

Solution for (3x+3)(5x-2)=180 equation:

(3x+3)(5x-2)=180

We move all terms to the left:

(3x+3)(5x-2)-(180)=0

We multiply parentheses ..

(+15x^2-6x+15x-6)-180=0

We get rid of parentheses

15x^2-6x+15x-6-180=0

We add all the numbers together, and all the variables

15x^2+9x-186=0

a = 15; b = 9; c = -186;
Δ = b2-4ac
Δ = 92-4·15·(-186)
Δ = 11241
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:

$\sqrt{\Delta}=\sqrt{11241}=\sqrt{9*1249}=\sqrt{9}*\sqrt{1249}=3\sqrt{1249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{1249}}{2*15}=\frac{-9-3\sqrt{1249}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{1249}}{2*15}=\frac{-9+3\sqrt{1249}}{30}
$