3x^2+2x=108

Solution for 3x^2+2x=108 equation:

3x^2+2x=108

We move all terms to the left:

3x^2+2x-(108)=0

a = 3; b = 2; c = -108;
Δ = b2-4ac
Δ = 22-4·3·(-108)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10\sqrt{13}}{2*3}=\frac{-2-10\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10\sqrt{13}}{2*3}=\frac{-2+10\sqrt{13}}{6}
$