(2x-2)+(x+1)+x(x+1)=55

Solution for (2x-2)+(x+1)+x(x+1)=55 equation:

(2x-2)+(x+1)+x(x+1)=55

We move all terms to the left:

(2x-2)+(x+1)+x(x+1)-(55)=0

We multiply parentheses

x^2+(2x-2)+(x+1)+x-55=0

We get rid of parentheses

x^2+2x+x+x-2+1-55=0

We add all the numbers together, and all the variables

x^2+4x-56=0

a = 1; b = 4; c = -56;
Δ = b2-4ac
Δ = 42-4·1·(-56)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{15}}{2*1}=\frac{-4-4\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{15}}{2*1}=\frac{-4+4\sqrt{15}}{2}
$