(6x-1)(11x+4)+75=180

Solution for (6x-1)(11x+4)+75=180 equation:

(6x-1)(11x+4)+75=180

We move all terms to the left:

(6x-1)(11x+4)+75-(180)=0

We add all the numbers together, and all the variables

(6x-1)(11x+4)-105=0

We multiply parentheses ..

(+66x^2+24x-11x-4)-105=0

We get rid of parentheses

66x^2+24x-11x-4-105=0

We add all the numbers together, and all the variables

66x^2+13x-109=0

a = 66; b = 13; c = -109;
Δ = b2-4ac
Δ = 132-4·66·(-109)
Δ = 28945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{28945}}{2*66}=\frac{-13-\sqrt{28945}}{132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{28945}}{2*66}=\frac{-13+\sqrt{28945}}{132}
$