38=3x^2+x-6

Solution for 38=3x^2+x-6 equation:

38=3x^2+x-6

We move all terms to the left:

38-(3x^2+x-6)=0

We get rid of parentheses

-3x^2-x+6+38=0

We add all the numbers together, and all the variables

-3x^2-1x+44=0

a = -3; b = -1; c = +44;
Δ = b2-4ac
Δ = -12-4·(-3)·44
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-23}{2*-3}=\frac{-22}{-6}
=3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+23}{2*-3}=\frac{24}{-6}
=-4
$