12x^2+6x=216

Solution for 12x^2+6x=216 equation:

12x^2+6x=216

We move all terms to the left:

12x^2+6x-(216)=0

a = 12; b = 6; c = -216;
Δ = b2-4ac
Δ = 62-4·12·(-216)
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-102}{2*12}=\frac{-108}{24}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+102}{2*12}=\frac{96}{24}
=4
$