2+6x2=3x+3

Solution for 2+6x2=3x+3 equation:

2+6x^2=3x+3

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2-3x-1=0

a = 6; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·6·(-1)
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*6}=\frac{3-\sqrt{33}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*6}=\frac{3+\sqrt{33}}{12}
$