6=2x^2+3x+3

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

6=2x^2+3x+3

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -3; c = +3;
Δ = b2-4ac
Δ = -32-4·(-2)·3
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*-2}=\frac{3-\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*-2}=\frac{3+\sqrt{33}}{-4}
$