2x+117=x^2

Solution for 2x+117=x^2 equation:

2x+117=x^2

We move all terms to the left:

2x+117-(x^2)=0

determiningTheFunctionDomain
-x^2+2x+117=0

We add all the numbers together, and all the variables

-1x^2+2x+117=0

a = -1; b = 2; c = +117;
Δ = b2-4ac
Δ = 22-4·(-1)·117
Δ = 472
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:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{118}}{2*-1}=\frac{-2-2\sqrt{118}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{118}}{2*-1}=\frac{-2+2\sqrt{118}}{-2}
$