54=3x^2+2x

Solution for 54=3x^2+2x equation:

54=3x^2+2x

We move all terms to the left:

54-(3x^2+2x)=0

We get rid of parentheses

-3x^2-2x+54=0

a = -3; b = -2; c = +54;
Δ = b2-4ac
Δ = -22-4·(-3)·54
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{163}}{2*-3}=\frac{2-2\sqrt{163}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{163}}{2*-3}=\frac{2+2\sqrt{163}}{-6}
$