(8x+35)(11x+23)=120

Solution for (8x+35)(11x+23)=120 equation:

(8x+35)(11x+23)=120

We move all terms to the left:

(8x+35)(11x+23)-(120)=0

We multiply parentheses ..

(+88x^2+184x+385x+805)-120=0

We get rid of parentheses

88x^2+184x+385x+805-120=0

We add all the numbers together, and all the variables

88x^2+569x+685=0

a = 88; b = 569; c = +685;
Δ = b2-4ac
Δ = 5692-4·88·685
Δ = 82641
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:

$\sqrt{\Delta}=\sqrt{82641}=\sqrt{169*489}=\sqrt{169}*\sqrt{489}=13\sqrt{489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(569)-13\sqrt{489}}{2*88}=\frac{-569-13\sqrt{489}}{176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(569)+13\sqrt{489}}{2*88}=\frac{-569+13\sqrt{489}}{176}
$