x^2-x=650

Solution for x^2-x=650 equation:

x^2-x=650

We move all terms to the left:

x^2-x-(650)=0

We add all the numbers together, and all the variables

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