32=6x^2+4x

Solution for 32=6x^2+4x equation:

32=6x^2+4x

We move all terms to the left:

32-(6x^2+4x)=0

We get rid of parentheses

-6x^2-4x+32=0

a = -6; b = -4; c = +32;
Δ = b2-4ac
Δ = -42-4·(-6)·32
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*-6}=\frac{32}{-12}
=-2+2/3
$