3.1x^2-5.5x=-2

Solution for 3.1x^2-5.5x=-2 equation:

3.1x^2-5.5x=-2

We move all terms to the left:

3.1x^2-5.5x-(-2)=0

We add all the numbers together, and all the variables

3.1x^2-5.5x+2=0

a = 3.1; b = -5.5; c = +2;
Δ = b2-4ac
Δ = -5.52-4·3.1·2
Δ = 5.45
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{-(-5.5)-\sqrt{5.45}}{2*3.1}=\frac{5.5-\sqrt{5.45}}{6.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.5)+\sqrt{5.45}}{2*3.1}=\frac{5.5+\sqrt{5.45}}{6.2}
$