(3x+5)(x+15)=180

Solution for (3x+5)(x+15)=180 equation:

(3x+5)(x+15)=180

We move all terms to the left:

(3x+5)(x+15)-(180)=0

We multiply parentheses ..

(+3x^2+45x+5x+75)-180=0

We get rid of parentheses

3x^2+45x+5x+75-180=0

We add all the numbers together, and all the variables

3x^2+50x-105=0

a = 3; b = 50; c = -105;
Δ = b2-4ac
Δ = 502-4·3·(-105)
Δ = 3760
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:

$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-4\sqrt{235}}{2*3}=\frac{-50-4\sqrt{235}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+4\sqrt{235}}{2*3}=\frac{-50+4\sqrt{235}}{6}
$