(4x-5)(3x+11)=180

Solution for (4x-5)(3x+11)=180 equation:

(4x-5)(3x+11)=180

We move all terms to the left:

(4x-5)(3x+11)-(180)=0

We multiply parentheses ..

(+12x^2+44x-15x-55)-180=0

We get rid of parentheses

12x^2+44x-15x-55-180=0

We add all the numbers together, and all the variables

12x^2+29x-235=0

a = 12; b = 29; c = -235;
Δ = b2-4ac
Δ = 292-4·12·(-235)
Δ = 12121
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{-(29)-\sqrt{12121}}{2*12}=\frac{-29-\sqrt{12121}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{12121}}{2*12}=\frac{-29+\sqrt{12121}}{24}
$