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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+12x^2+20x-15x-25)-180=0

We get rid of parentheses

12x^2+20x-15x-25-180=0

We add all the numbers together, and all the variables

12x^2+5x-205=0

a = 12; b = 5; c = -205;
Δ = b2-4ac
Δ = 52-4·12·(-205)
Δ = 9865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{9865}}{2*12}=\frac{-5-\sqrt{9865}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{9865}}{2*12}=\frac{-5+\sqrt{9865}}{24}
$