(7x+9)(9x-23)=180

Solution for (7x+9)(9x-23)=180 equation:

(7x+9)(9x-23)=180

We move all terms to the left:

(7x+9)(9x-23)-(180)=0

We multiply parentheses ..

(+63x^2-161x+81x-207)-180=0

We get rid of parentheses

63x^2-161x+81x-207-180=0

We add all the numbers together, and all the variables

63x^2-80x-387=0

a = 63; b = -80; c = -387;
Δ = b2-4ac
Δ = -802-4·63·(-387)
Δ = 103924
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:

$\sqrt{\Delta}=\sqrt{103924}=\sqrt{4*25981}=\sqrt{4}*\sqrt{25981}=2\sqrt{25981}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{25981}}{2*63}=\frac{80-2\sqrt{25981}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{25981}}{2*63}=\frac{80+2\sqrt{25981}}{126}
$