x^2-x=(-42)^2-(-42)

Solution for x^2-x=(-42)^2-(-42) equation:

x^2-x=(-42)^2-(-42)

We move all terms to the left:

x^2-x-((-42)^2-(-42))=0

We add all the numbers together, and all the variables

x^2-1x-1806=0

a = 1; b = -1; c = -1806;
Δ = b2-4ac
Δ = -12-4·1·(-1806)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-85}{2*1}=\frac{-84}{2}
=-42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+85}{2*1}=\frac{86}{2}
=43
$