x^2+2x+1=7918-2x

Solution for x^2+2x+1=7918-2x equation:

x^2+2x+1=7918-2x

We move all terms to the left:

x^2+2x+1-(7918-2x)=0

We add all the numbers together, and all the variables

x^2+2x-(-2x+7918)+1=0

We get rid of parentheses

x^2+2x+2x-7918+1=0

We add all the numbers together, and all the variables

x^2+4x-7917=0

a = 1; b = 4; c = -7917;
Δ = b2-4ac
Δ = 42-4·1·(-7917)
Δ = 31684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{31684}=178$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-178}{2*1}=\frac{-182}{2}
=-91
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+178}{2*1}=\frac{174}{2}
=87
$