(3x-11)(x+43)=180

Solution for (3x-11)(x+43)=180 equation:

(3x-11)(x+43)=180

We move all terms to the left:

(3x-11)(x+43)-(180)=0

We multiply parentheses ..

(+3x^2+129x-11x-473)-180=0

We get rid of parentheses

3x^2+129x-11x-473-180=0

We add all the numbers together, and all the variables

3x^2+118x-653=0

a = 3; b = 118; c = -653;
Δ = b2-4ac
Δ = 1182-4·3·(-653)
Δ = 21760
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:

$\sqrt{\Delta}=\sqrt{21760}=\sqrt{256*85}=\sqrt{256}*\sqrt{85}=16\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(118)-16\sqrt{85}}{2*3}=\frac{-118-16\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(118)+16\sqrt{85}}{2*3}=\frac{-118+16\sqrt{85}}{6}
$