420=q^2-q

Solution for 420=q^2-q equation:

420=q^2-q

We move all terms to the left:

420-(q^2-q)=0

We get rid of parentheses

-q^2+q+420=0

We add all the numbers together, and all the variables

-1q^2+q+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:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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