X^2+x=2500

Solution for X^2+x=2500 equation:

X^2+X=2500

We move all terms to the left:

X^2+X-(2500)=0

a = 1; b = 1; c = -2500;
Δ = b2-4ac
Δ = 12-4·1·(-2500)
Δ = 10001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{10001}}{2*1}=\frac{-1-\sqrt{10001}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{10001}}{2*1}=\frac{-1+\sqrt{10001}}{2}
$