(2x+15)(6x-10)=180

Solution for (2x+15)(6x-10)=180 equation:

(2x+15)(6x-10)=180

We move all terms to the left:

(2x+15)(6x-10)-(180)=0

We multiply parentheses ..

(+12x^2-20x+90x-150)-180=0

We get rid of parentheses

12x^2-20x+90x-150-180=0

We add all the numbers together, and all the variables

12x^2+70x-330=0

a = 12; b = 70; c = -330;
Δ = b2-4ac
Δ = 702-4·12·(-330)
Δ = 20740
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:

$\sqrt{\Delta}=\sqrt{20740}=\sqrt{4*5185}=\sqrt{4}*\sqrt{5185}=2\sqrt{5185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{5185}}{2*12}=\frac{-70-2\sqrt{5185}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{5185}}{2*12}=\frac{-70+2\sqrt{5185}}{24}
$