(7x-2)(11x-34)=180

Solution for (7x-2)(11x-34)=180 equation:

(7x-2)(11x-34)=180

We move all terms to the left:

(7x-2)(11x-34)-(180)=0

We multiply parentheses ..

(+77x^2-238x-22x+68)-180=0

We get rid of parentheses

77x^2-238x-22x+68-180=0

We add all the numbers together, and all the variables

77x^2-260x-112=0

a = 77; b = -260; c = -112;
Δ = b2-4ac
Δ = -2602-4·77·(-112)
Δ = 102096
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:

$\sqrt{\Delta}=\sqrt{102096}=\sqrt{144*709}=\sqrt{144}*\sqrt{709}=12\sqrt{709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-12\sqrt{709}}{2*77}=\frac{260-12\sqrt{709}}{154}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+12\sqrt{709}}{2*77}=\frac{260+12\sqrt{709}}{154}
$