(5x-8)(3x+4)=180

Solution for (5x-8)(3x+4)=180 equation:

(5x-8)(3x+4)=180

We move all terms to the left:

(5x-8)(3x+4)-(180)=0

We multiply parentheses ..

(+15x^2+20x-24x-32)-180=0

We get rid of parentheses

15x^2+20x-24x-32-180=0

We add all the numbers together, and all the variables

15x^2-4x-212=0

a = 15; b = -4; c = -212;
Δ = b2-4ac
Δ = -42-4·15·(-212)
Δ = 12736
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:

$\sqrt{\Delta}=\sqrt{12736}=\sqrt{64*199}=\sqrt{64}*\sqrt{199}=8\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{199}}{2*15}=\frac{4-8\sqrt{199}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{199}}{2*15}=\frac{4+8\sqrt{199}}{30}
$