(3x+11)(x+21)=180

Solution for (3x+11)(x+21)=180 equation:

(3x+11)(x+21)=180

We move all terms to the left:

(3x+11)(x+21)-(180)=0

We multiply parentheses ..

(+3x^2+63x+11x+231)-180=0

We get rid of parentheses

3x^2+63x+11x+231-180=0

We add all the numbers together, and all the variables

3x^2+74x+51=0

a = 3; b = 74; c = +51;
Δ = b2-4ac
Δ = 742-4·3·51
Δ = 4864
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:

$\sqrt{\Delta}=\sqrt{4864}=\sqrt{256*19}=\sqrt{256}*\sqrt{19}=16\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-16\sqrt{19}}{2*3}=\frac{-74-16\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+16\sqrt{19}}{2*3}=\frac{-74+16\sqrt{19}}{6}
$