27x-54=-6x^2

Solution for 27x-54=-6x^2 equation:

27x-54=-6x^2

We move all terms to the left:

27x-54-(-6x^2)=0

We get rid of parentheses

6x^2+27x-54=0

a = 6; b = 27; c = -54;
Δ = b2-4ac
Δ = 272-4·6·(-54)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-45}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+45}{2*6}=\frac{18}{12}
=1+1/2
$