12x^2+54x+36=-6

Solution for 12x^2+54x+36=-6 equation:

12x^2+54x+36=-6

We move all terms to the left:

12x^2+54x+36-(-6)=0

We add all the numbers together, and all the variables

12x^2+54x+42=0

a = 12; b = 54; c = +42;
Δ = b2-4ac
Δ = 542-4·12·42
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-30}{2*12}=\frac{-84}{24}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+30}{2*12}=\frac{-24}{24}
=-1
$