X+x^2=200000

Solution for X+x^2=200000 equation:

X+X^2=200000

We move all terms to the left:

X+X^2-(200000)=0

a = 1; b = 1; c = -200000;
Δ = b2-4ac
Δ = 12-4·1·(-200000)
Δ = 800001
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:

$\sqrt{\Delta}=\sqrt{800001}=\sqrt{9*88889}=\sqrt{9}*\sqrt{88889}=3\sqrt{88889}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{88889}}{2*1}=\frac{-1-3\sqrt{88889}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{88889}}{2*1}=\frac{-1+3\sqrt{88889}}{2}
$