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

Solution for (x^2)+18x-189=0 equation:

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

a = 1; b = 18; c = -189;
Δ = b2-4ac
Δ = 182-4·1·(-189)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{30}}{2*1}=\frac{-18-6\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{30}}{2*1}=\frac{-18+6\sqrt{30}}{2}
$