(x+47)(2x-11)+x=180

Solution for (x+47)(2x-11)+x=180 equation:

(x+47)(2x-11)+x=180

We move all terms to the left:

(x+47)(2x-11)+x-(180)=0

We add all the numbers together, and all the variables

x+(x+47)(2x-11)-180=0

We multiply parentheses ..

(+2x^2-11x+94x-517)+x-180=0

We get rid of parentheses

2x^2-11x+94x+x-517-180=0

We add all the numbers together, and all the variables

2x^2+84x-697=0

a = 2; b = 84; c = -697;
Δ = b2-4ac
Δ = 842-4·2·(-697)
Δ = 12632
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:

$\sqrt{\Delta}=\sqrt{12632}=\sqrt{4*3158}=\sqrt{4}*\sqrt{3158}=2\sqrt{3158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-2\sqrt{3158}}{2*2}=\frac{-84-2\sqrt{3158}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+2\sqrt{3158}}{2*2}=\frac{-84+2\sqrt{3158}}{4}
$