27x=-3x^2-54

Solution for 27x=-3x^2-54 equation:

27x=-3x^2-54

We move all terms to the left:

27x-(-3x^2-54)=0

We get rid of parentheses

3x^2+27x+54=0

a = 3; b = 27; c = +54;
Δ = b2-4ac
Δ = 272-4·3·54
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-9}{2*3}=\frac{-36}{6}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+9}{2*3}=\frac{-18}{6}
=-3
$