x+x^2=650

Solution for x+x^2=650 equation:

x+x^2=650

We move all terms to the left:

x+x^2-(650)=0

a = 1; b = 1; c = -650;
Δ = b2-4ac
Δ = 12-4·1·(-650)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-51}{2*1}=\frac{-52}{2}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+51}{2*1}=\frac{50}{2}
=25
$