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

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

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

We move all terms to the left:

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

We get rid of parentheses

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