5.5x+3x2-15+2x=x

Solution for 5.5x+3x2-15+2x=x equation:

5.5x+3x^2-15+2x=x

We move all terms to the left:

5.5x+3x^2-15+2x-(x)=0

We add all the numbers together, and all the variables

3x^2+6.5x-15=0

a = 3; b = 6.5; c = -15;
Δ = b2-4ac
Δ = 6.52-4·3·(-15)
Δ = 222.25
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{-(6.5)-\sqrt{222.25}}{2*3}=\frac{-6.5-\sqrt{222.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.5)+\sqrt{222.25}}{2*3}=\frac{-6.5+\sqrt{222.25}}{6}
$