1/6x+1/9x=1

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

1/6x+1/9x=1

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We calculate fractions


9x/54x^2+6x/54x^2-1=0

We multiply all the terms by the denominator


9x+6x-1*54x^2=0

We add all the numbers together, and all the variables

15x-1*54x^2=0

Wy multiply elements

-54x^2+15x=0

a = -54; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-54)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-54}=\frac{-30}{-108}
=5/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-54}=\frac{0}{-108}
=0
$