3x^2+18x+27=5

Solution for 3x^2+18x+27=5 equation:

3x^2+18x+27=5

We move all terms to the left:

3x^2+18x+27-(5)=0

We add all the numbers together, and all the variables

3x^2+18x+22=0

a = 3; b = 18; c = +22;
Δ = b2-4ac
Δ = 182-4·3·22
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{15}}{2*3}=\frac{-18-2\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{15}}{2*3}=\frac{-18+2\sqrt{15}}{6}
$