(3x+15)(2x+20)=180

Solution for (3x+15)(2x+20)=180 equation:

(3x+15)(2x+20)=180

We move all terms to the left:

(3x+15)(2x+20)-(180)=0

We multiply parentheses ..

(+6x^2+60x+30x+300)-180=0

We get rid of parentheses

6x^2+60x+30x+300-180=0

We add all the numbers together, and all the variables

6x^2+90x+120=0

a = 6; b = 90; c = +120;
Δ = b2-4ac
Δ = 902-4·6·120
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{145}}{2*6}=\frac{-90-6\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{145}}{2*6}=\frac{-90+6\sqrt{145}}{12}
$