(5x+6)(3x-2)=180

Solution for (5x+6)(3x-2)=180 equation:

(5x+6)(3x-2)=180

We move all terms to the left:

(5x+6)(3x-2)-(180)=0

We multiply parentheses ..

(+15x^2-10x+18x-12)-180=0

We get rid of parentheses

15x^2-10x+18x-12-180=0

We add all the numbers together, and all the variables

15x^2+8x-192=0

a = 15; b = 8; c = -192;
Δ = b2-4ac
Δ = 82-4·15·(-192)
Δ = 11584
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:

$\sqrt{\Delta}=\sqrt{11584}=\sqrt{64*181}=\sqrt{64}*\sqrt{181}=8\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{181}}{2*15}=\frac{-8-8\sqrt{181}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{181}}{2*15}=\frac{-8+8\sqrt{181}}{30}
$