(7x+6)(9x-24)=180

Solution for (7x+6)(9x-24)=180 equation:

(7x+6)(9x-24)=180

We move all terms to the left:

(7x+6)(9x-24)-(180)=0

We multiply parentheses ..

(+63x^2-168x+54x-144)-180=0

We get rid of parentheses

63x^2-168x+54x-144-180=0

We add all the numbers together, and all the variables

63x^2-114x-324=0

a = 63; b = -114; c = -324;
Δ = b2-4ac
Δ = -1142-4·63·(-324)
Δ = 94644
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:

$\sqrt{\Delta}=\sqrt{94644}=\sqrt{36*2629}=\sqrt{36}*\sqrt{2629}=6\sqrt{2629}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{2629}}{2*63}=\frac{114-6\sqrt{2629}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{2629}}{2*63}=\frac{114+6\sqrt{2629}}{126}
$