3+x=5.5+2/9x

Solution for 3+x=5.5+2/9x equation:

3+x=5.5+2/9x

We move all terms to the left:

3+x-(5.5+2/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(2/9x+5.5)+3=0

We get rid of parentheses

x-2/9x-5.5+3=0

We multiply all the terms by the denominator


x*9x-(5.5)*9x+3*9x-2=0

We multiply parentheses

x*9x-49.5x+3*9x-2=0

Wy multiply elements

9x^2-49.5x+27x-2=0

We add all the numbers together, and all the variables

9x^2-22.5x-2=0

a = 9; b = -22.5; c = -2;
Δ = b2-4ac
Δ = -22.52-4·9·(-2)
Δ = 578.25
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{-(-22.5)-\sqrt{578.25}}{2*9}=\frac{22.5-\sqrt{578.25}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22.5)+\sqrt{578.25}}{2*9}=\frac{22.5+\sqrt{578.25}}{18}
$