X^2+2x+100=460

Solution for X^2+2x+100=460 equation:

X^2+2X+100=460

We move all terms to the left:

X^2+2X+100-(460)=0

We add all the numbers together, and all the variables

X^2+2X-360=0

a = 1; b = 2; c = -360;
Δ = b2-4ac
Δ = 22-4·1·(-360)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*1}=\frac{-40}{2}
=-20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*1}=\frac{36}{2}
=18
$