x^2-x=420

Solution for x^2-x=420 equation:

x^2-x=420

We move all terms to the left:

x^2-x-(420)=0

We add all the numbers together, and all the variables

x^2-1x-420=0

a = 1; b = -1; c = -420;
Δ = b2-4ac
Δ = -12-4·1·(-420)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-41}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+41}{2*1}=\frac{42}{2}
=21
$