X2+18x+1=0

Solution for X2+18x+1=0 equation:

X2+18X+1=0

We add all the numbers together, and all the variables

X^2+18X+1=0

a = 1; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·1·1
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-8\sqrt{5}}{2*1}=\frac{-18-8\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+8\sqrt{5}}{2*1}=\frac{-18+8\sqrt{5}}{2}
$