x^2+6x+27=360

Solution for x^2+6x+27=360 equation:

x^2+6x+27=360

We move all terms to the left:

x^2+6x+27-(360)=0

We add all the numbers together, and all the variables

x^2+6x-333=0

a = 1; b = 6; c = -333;
Δ = b2-4ac
Δ = 62-4·1·(-333)
Δ = 1368
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:

$\sqrt{\Delta}=\sqrt{1368}=\sqrt{36*38}=\sqrt{36}*\sqrt{38}=6\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{38}}{2*1}=\frac{-6-6\sqrt{38}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{38}}{2*1}=\frac{-6+6\sqrt{38}}{2}
$