(3x+6)(5x-10)=180

Solution for (3x+6)(5x-10)=180 equation:

(3x+6)(5x-10)=180

We move all terms to the left:

(3x+6)(5x-10)-(180)=0

We multiply parentheses ..

(+15x^2-30x+30x-60)-180=0

We get rid of parentheses

15x^2-30x+30x-60-180=0

We add all the numbers together, and all the variables

15x^2-240=0

a = 15; b = 0; c = -240;
Δ = b2-4ac
Δ = 02-4·15·(-240)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120}{2*15}=\frac{-120}{30}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120}{2*15}=\frac{120}{30}
=4
$