(7x-15)(24x+9)=180

Solution for (7x-15)(24x+9)=180 equation:

(7x-15)(24x+9)=180

We move all terms to the left:

(7x-15)(24x+9)-(180)=0

We multiply parentheses ..

(+168x^2+63x-360x-135)-180=0

We get rid of parentheses

168x^2+63x-360x-135-180=0

We add all the numbers together, and all the variables

168x^2-297x-315=0

a = 168; b = -297; c = -315;
Δ = b2-4ac
Δ = -2972-4·168·(-315)
Δ = 299889
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:

$\sqrt{\Delta}=\sqrt{299889}=\sqrt{9*33321}=\sqrt{9}*\sqrt{33321}=3\sqrt{33321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-297)-3\sqrt{33321}}{2*168}=\frac{297-3\sqrt{33321}}{336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-297)+3\sqrt{33321}}{2*168}=\frac{297+3\sqrt{33321}}{336}
$