(11x-28)(7x-8)=180

Solution for (11x-28)(7x-8)=180 equation:

(11x-28)(7x-8)=180

We move all terms to the left:

(11x-28)(7x-8)-(180)=0

We multiply parentheses ..

(+77x^2-88x-196x+224)-180=0

We get rid of parentheses

77x^2-88x-196x+224-180=0

We add all the numbers together, and all the variables

77x^2-284x+44=0

a = 77; b = -284; c = +44;
Δ = b2-4ac
Δ = -2842-4·77·44
Δ = 67104
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:

$\sqrt{\Delta}=\sqrt{67104}=\sqrt{144*466}=\sqrt{144}*\sqrt{466}=12\sqrt{466}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-284)-12\sqrt{466}}{2*77}=\frac{284-12\sqrt{466}}{154}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-284)+12\sqrt{466}}{2*77}=\frac{284+12\sqrt{466}}{154}
$