X^2+18x=-27

Solution for X^2+18x=-27 equation:

X^2+18X=-27

We move all terms to the left:

X^2+18X-(-27)=0

We add all the numbers together, and all the variables

X^2+18X+27=0

a = 1; b = 18; c = +27;
Δ = b2-4ac
Δ = 182-4·1·27
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{6}}{2*1}=\frac{-18-6\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{6}}{2*1}=\frac{-18+6\sqrt{6}}{2}
$