308=3x^2+2x

Solution for 308=3x^2+2x equation:

308=3x^2+2x

We move all terms to the left:

308-(3x^2+2x)=0

We get rid of parentheses

-3x^2-2x+308=0

a = -3; b = -2; c = +308;
Δ = b2-4ac
Δ = -22-4·(-3)·308
Δ = 3700
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:

$\sqrt{\Delta}=\sqrt{3700}=\sqrt{100*37}=\sqrt{100}*\sqrt{37}=10\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10\sqrt{37}}{2*-3}=\frac{2-10\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10\sqrt{37}}{2*-3}=\frac{2+10\sqrt{37}}{-6}
$