9/2x+18+3x=5.5

Solution for 9/2x+18+3x=5.5 equation:

9/2x+18+3x=5.5

We move all terms to the left:

9/2x+18+3x-(5.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+9/2x+12.5=0

We multiply all the terms by the denominator


3x*2x+(12.5)*2x+9=0

We multiply parentheses

3x*2x+25x+9=0

Wy multiply elements

6x^2+25x+9=0

a = 6; b = 25; c = +9;
Δ = b2-4ac
Δ = 252-4·6·9
Δ = 409
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{-(25)-\sqrt{409}}{2*6}=\frac{-25-\sqrt{409}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{409}}{2*6}=\frac{-25+\sqrt{409}}{12}
$