3X^2-x=2x+2

Solution for 3X^2-x=2x+2 equation:

3X^2-X=2X+2

We move all terms to the left:

3X^2-X-(2X+2)=0

We add all the numbers together, and all the variables

3X^2-1X-(2X+2)=0

We get rid of parentheses

3X^2-1X-2X-2=0

We add all the numbers together, and all the variables

3X^2-3X-2=0

a = 3; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·3·(-2)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{33}}{2*3}=\frac{3-\sqrt{33}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*3}=\frac{3+\sqrt{33}}{6}
$