3x-1/9x+1=0

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

3x-1/9x+1=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

27x^2+9x-1=0

a = 27; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·27·(-1)
Δ = 189
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{21}}{2*27}=\frac{-9-3\sqrt{21}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{21}}{2*27}=\frac{-9+3\sqrt{21}}{54}
$