(8x+7)(9x-4)=180

Solution for (8x+7)(9x-4)=180 equation:

(8x+7)(9x-4)=180

We move all terms to the left:

(8x+7)(9x-4)-(180)=0

We multiply parentheses ..

(+72x^2-32x+63x-28)-180=0

We get rid of parentheses

72x^2-32x+63x-28-180=0

We add all the numbers together, and all the variables

72x^2+31x-208=0

a = 72; b = 31; c = -208;
Δ = b2-4ac
Δ = 312-4·72·(-208)
Δ = 60865
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{-(31)-\sqrt{60865}}{2*72}=\frac{-31-\sqrt{60865}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{60865}}{2*72}=\frac{-31+\sqrt{60865}}{144}
$