x(x-2018)+x-2018=0

Solution for x(x-2018)+x-2018=0 equation:

x(x-2018)+x-2018=0

We add all the numbers together, and all the variables

x+x(x-2018)-2018=0

We multiply parentheses

x^2+x-2018x-2018=0

We add all the numbers together, and all the variables

x^2-2017x-2018=0

a = 1; b = -2017; c = -2018;
Δ = b2-4ac
Δ = -20172-4·1·(-2018)
Δ = 4076361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4076361}=2019$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2017)-2019}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2017)+2019}{2*1}=\frac{4036}{2}
=2018
$