X^2=2x+115

Solution for X^2=2x+115 equation:

X^2=2X+115

We move all terms to the left:

X^2-(2X+115)=0

We get rid of parentheses

X^2-2X-115=0

a = 1; b = -2; c = -115;
Δ = b2-4ac
Δ = -22-4·1·(-115)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{29}}{2*1}=\frac{2-4\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{29}}{2*1}=\frac{2+4\sqrt{29}}{2}
$