5.5=3x^2-x

Solution for 5.5=3x^2-x equation:

5.5=3x^2-x

We move all terms to the left:

5.5-(3x^2-x)=0

We get rid of parentheses

-3x^2+x+5.5=0

a = -3; b = 1; c = +5.5;
Δ = b2-4ac
Δ = 12-4·(-3)·5.5
Δ = 67
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{67}}{2*-3}=\frac{-1-\sqrt{67}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{67}}{2*-3}=\frac{-1+\sqrt{67}}{-6}
$