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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+77x^2-22x+14x-4)-180=0

We get rid of parentheses

77x^2-22x+14x-4-180=0

We add all the numbers together, and all the variables

77x^2-8x-184=0

a = 77; b = -8; c = -184;
Δ = b2-4ac
Δ = -82-4·77·(-184)
Δ = 56736
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:

$\sqrt{\Delta}=\sqrt{56736}=\sqrt{144*394}=\sqrt{144}*\sqrt{394}=12\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{394}}{2*77}=\frac{8-12\sqrt{394}}{154}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{394}}{2*77}=\frac{8+12\sqrt{394}}{154}
$