x^2+9x+18=189

Solution for x^2+9x+18=189 equation:

x^2+9x+18=189

We move all terms to the left:

x^2+9x+18-(189)=0

We add all the numbers together, and all the variables

x^2+9x-171=0

a = 1; b = 9; c = -171;
Δ = b2-4ac
Δ = 92-4·1·(-171)
Δ = 765
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:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{85}}{2*1}=\frac{-9-3\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{85}}{2*1}=\frac{-9+3\sqrt{85}}{2}
$