(8x-7)(9x-28)=180

Solution for (8x-7)(9x-28)=180 equation:

(8x-7)(9x-28)=180

We move all terms to the left:

(8x-7)(9x-28)-(180)=0

We multiply parentheses ..

(+72x^2-224x-63x+196)-180=0

We get rid of parentheses

72x^2-224x-63x+196-180=0

We add all the numbers together, and all the variables

72x^2-287x+16=0

a = 72; b = -287; c = +16;
Δ = b2-4ac
Δ = -2872-4·72·16
Δ = 77761
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{-(-287)-\sqrt{77761}}{2*72}=\frac{287-\sqrt{77761}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-287)+\sqrt{77761}}{2*72}=\frac{287+\sqrt{77761}}{144}
$