2/x+5/3x=9

Solution for 2/x+5/3x=9 equation:

2/x+5/3x=9

We move all terms to the left:

2/x+5/3x-(9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


6x/3x^2+5x/3x^2-9=0

We multiply all the terms by the denominator


6x+5x-9*3x^2=0

We add all the numbers together, and all the variables

11x-9*3x^2=0

Wy multiply elements

-27x^2+11x=0

a = -27; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-27)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-27}=\frac{-22}{-54}
=11/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-27}=\frac{0}{-54}
=0
$