-1/2x+5.5=-x

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

-1/2x+5.5=-x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We multiply parentheses

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

Wy multiply elements

2x^2+11x-1=0

a = 2; b = 11; c = -1;
Δ = b2-4ac
Δ = 112-4·2·(-1)
Δ = 129
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{-(11)-\sqrt{129}}{2*2}=\frac{-11-\sqrt{129}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{129}}{2*2}=\frac{-11+\sqrt{129}}{4}
$