9x-1/3x+2=0

Solution for 9x-1/3x+2=0 equation:

9x-1/3x+2=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


9x*3x+2*3x-1=0

Wy multiply elements

27x^2+6x-1=0

a = 27; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·27·(-1)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*27}=\frac{-18}{54}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*27}=\frac{6}{54}
=1/9
$