x^2+18x=164

Solution for x^2+18x=164 equation:

x^2+18x=164

We move all terms to the left:

x^2+18x-(164)=0

a = 1; b = 18; c = -164;
Δ = b2-4ac
Δ = 182-4·1·(-164)
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-14\sqrt{5}}{2*1}=\frac{-18-14\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+14\sqrt{5}}{2*1}=\frac{-18+14\sqrt{5}}{2}
$