18x^2+27x=12

Solution for 18x^2+27x=12 equation:

18x^2+27x=12

We move all terms to the left:

18x^2+27x-(12)=0

a = 18; b = 27; c = -12;
Δ = b2-4ac
Δ = 272-4·18·(-12)
Δ = 1593
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:

$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{177}}{2*18}=\frac{-27-3\sqrt{177}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{177}}{2*18}=\frac{-27+3\sqrt{177}}{36}
$