x^2-x=2018

Solution for x^2-x=2018 equation:

x^2-x=2018

We move all terms to the left:

x^2-x-(2018)=0

We add all the numbers together, and all the variables

x^2-1x-2018=0

a = 1; b = -1; c = -2018;
Δ = b2-4ac
Δ = -12-4·1·(-2018)
Δ = 8073
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8073}=\sqrt{9*897}=\sqrt{9}*\sqrt{897}=3\sqrt{897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{897}}{2*1}=\frac{1-3\sqrt{897}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{897}}{2*1}=\frac{1+3\sqrt{897}}{2}
$