(7x+14)(9x-8)=180

Solution for (7x+14)(9x-8)=180 equation:

(7x+14)(9x-8)=180

We move all terms to the left:

(7x+14)(9x-8)-(180)=0

We multiply parentheses ..

(+63x^2-56x+126x-112)-180=0

We get rid of parentheses

63x^2-56x+126x-112-180=0

We add all the numbers together, and all the variables

63x^2+70x-292=0

a = 63; b = 70; c = -292;
Δ = b2-4ac
Δ = 702-4·63·(-292)
Δ = 78484
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:

$\sqrt{\Delta}=\sqrt{78484}=\sqrt{4*19621}=\sqrt{4}*\sqrt{19621}=2\sqrt{19621}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{19621}}{2*63}=\frac{-70-2\sqrt{19621}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{19621}}{2*63}=\frac{-70+2\sqrt{19621}}{126}
$