2/9x+1/6x^=1

Solution for 2/9x+1/6x^=1 equation:

2/9x+1/6x^=1

We move all terms to the left:

2/9x+1/6x^-(1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 6x^!=0

x!=0/6

x!=0

x∈R


We calculate fractions


12x/54x^2+9x/54x^2-1=0

We multiply all the terms by the denominator


12x+9x-1*54x^2=0

We add all the numbers together, and all the variables

21x-1*54x^2=0

Wy multiply elements

-54x^2+21x=0

a = -54; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-54)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-54}=\frac{-42}{-108}
=7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-54}=\frac{0}{-108}
=0
$