x^2+2x+100=360

Solution for x^2+2x+100=360 equation:

x^2+2x+100=360

We move all terms to the left:

x^2+2x+100-(360)=0

We add all the numbers together, and all the variables

x^2+2x-260=0

a = 1; b = 2; c = -260;
Δ = b2-4ac
Δ = 22-4·1·(-260)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{29}}{2*1}=\frac{-2-6\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{29}}{2*1}=\frac{-2+6\sqrt{29}}{2}
$