2x+5.5=22+1/2x

Solution for 2x+5.5=22+1/2x equation:

2x+5.5=22+1/2x

We move all terms to the left:

2x+5.5-(22+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(1/2x+22)+5.5=0

We get rid of parentheses

2x-1/2x-22+5.5=0

We multiply all the terms by the denominator


2x*2x-22*2x+(5.5)*2x-1=0

We multiply parentheses

2x*2x-22*2x+11x-1=0

Wy multiply elements

4x^2-44x+11x-1=0

We add all the numbers together, and all the variables

4x^2-33x-1=0

a = 4; b = -33; c = -1;
Δ = b2-4ac
Δ = -332-4·4·(-1)
Δ = 1105
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{-(-33)-\sqrt{1105}}{2*4}=\frac{33-\sqrt{1105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1105}}{2*4}=\frac{33+\sqrt{1105}}{8}
$