x+3=3x^2+3x-2

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

x+3=3x^2+3x-2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2-2x+5=0

a = -3; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-3)·5
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*-3}=\frac{10}{-6}
=-1+2/3
$