x*x-x=2652

Solution for x*x-x=2652 equation:

x*x-x=2652

We move all terms to the left:

x*x-x-(2652)=0

We add all the numbers together, and all the variables

-1x+x*x-2652=0

Wy multiply elements

x^2-1x-2652=0

a = 1; b = -1; c = -2652;
Δ = b2-4ac
Δ = -12-4·1·(-2652)
Δ = 10609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10609}=103$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-103}{2*1}=\frac{-102}{2}
=-51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+103}{2*1}=\frac{104}{2}
=52
$