x^2+18x-213=0

Solution for x^2+18x-213=0 equation:

x^2+18x-213=0

a = 1; b = 18; c = -213;
Δ = b2-4ac
Δ = 182-4·1·(-213)
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-14\sqrt{6}}{2*1}=\frac{-18-14\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+14\sqrt{6}}{2*1}=\frac{-18+14\sqrt{6}}{2}
$