5.5x+2/3x=27

Solution for 5.5x+2/3x=27 equation:

5.5x+2/3x=27

We move all terms to the left:

5.5x+2/3x-(27)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


(5.5x)*3x-27*3x+2=0

We add all the numbers together, and all the variables

(+5.5x)*3x-27*3x+2=0

We multiply parentheses

15x^2-27*3x+2=0

Wy multiply elements

15x^2-81x+2=0

a = 15; b = -81; c = +2;
Δ = b2-4ac
Δ = -812-4·15·2
Δ = 6441
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{-(-81)-\sqrt{6441}}{2*15}=\frac{81-\sqrt{6441}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+\sqrt{6441}}{2*15}=\frac{81+\sqrt{6441}}{30}
$