2-3x2+3=x

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

2-3x^2+3=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-3x^2-1x+5=0

a = -3; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-3)·5
Δ = 61
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{-(-1)-\sqrt{61}}{2*-3}=\frac{1-\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{61}}{2*-3}=\frac{1+\sqrt{61}}{-6}
$