(3x+24)(11x-40)=180

Solution for (3x+24)(11x-40)=180 equation:

(3x+24)(11x-40)=180

We move all terms to the left:

(3x+24)(11x-40)-(180)=0

We multiply parentheses ..

(+33x^2-120x+264x-960)-180=0

We get rid of parentheses

33x^2-120x+264x-960-180=0

We add all the numbers together, and all the variables

33x^2+144x-1140=0

a = 33; b = 144; c = -1140;
Δ = b2-4ac
Δ = 1442-4·33·(-1140)
Δ = 171216
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:

$\sqrt{\Delta}=\sqrt{171216}=\sqrt{144*1189}=\sqrt{144}*\sqrt{1189}=12\sqrt{1189}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-12\sqrt{1189}}{2*33}=\frac{-144-12\sqrt{1189}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+12\sqrt{1189}}{2*33}=\frac{-144+12\sqrt{1189}}{66}
$