(11x+2)(8x+7)=180

Solution for (11x+2)(8x+7)=180 equation:

(11x+2)(8x+7)=180

We move all terms to the left:

(11x+2)(8x+7)-(180)=0

We multiply parentheses ..

(+88x^2+77x+16x+14)-180=0

We get rid of parentheses

88x^2+77x+16x+14-180=0

We add all the numbers together, and all the variables

88x^2+93x-166=0

a = 88; b = 93; c = -166;
Δ = b2-4ac
Δ = 932-4·88·(-166)
Δ = 67081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67081}=259$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-259}{2*88}=\frac{-352}{176}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+259}{2*88}=\frac{166}{176}
=83/88
$