338=3x^2+2x+180

Solution for 338=3x^2+2x+180 equation:

338=3x^2+2x+180

We move all terms to the left:

338-(3x^2+2x+180)=0

We get rid of parentheses

-3x^2-2x-180+338=0

We add all the numbers together, and all the variables

-3x^2-2x+158=0

a = -3; b = -2; c = +158;
Δ = b2-4ac
Δ = -22-4·(-3)·158
Δ = 1900
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:

$\sqrt{\Delta}=\sqrt{1900}=\sqrt{100*19}=\sqrt{100}*\sqrt{19}=10\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10\sqrt{19}}{2*-3}=\frac{2-10\sqrt{19}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10\sqrt{19}}{2*-3}=\frac{2+10\sqrt{19}}{-6}
$