X^2=2019-x

Solution for X^2=2019-x equation:

X^2=2019-X

We move all terms to the left:

X^2-(2019-X)=0

We add all the numbers together, and all the variables

X^2-(-1X+2019)=0

We get rid of parentheses

X^2+1X-2019=0

We add all the numbers together, and all the variables

X^2+X-2019=0

a = 1; b = 1; c = -2019;
Δ = b2-4ac
Δ = 12-4·1·(-2019)
Δ = 8077
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{8077}}{2*1}=\frac{-1-\sqrt{8077}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{8077}}{2*1}=\frac{-1+\sqrt{8077}}{2}
$