X^2+18x+81=200

Solution for X^2+18x+81=200 equation:

X^2+18X+81=200

We move all terms to the left:

X^2+18X+81-(200)=0

We add all the numbers together, and all the variables

X^2+18X-119=0

a = 1; b = 18; c = -119;
Δ = b2-4ac
Δ = 182-4·1·(-119)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-20\sqrt{2}}{2*1}=\frac{-18-20\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+20\sqrt{2}}{2*1}=\frac{-18+20\sqrt{2}}{2}
$