1/9x-1/12x=1

Solution for 1/9x-1/12x=1 equation:

1/9x-1/12x=1

We move all terms to the left:

1/9x-1/12x-(1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We calculate fractions


12x/108x^2+(-9x)/108x^2-1=0

We multiply all the terms by the denominator


12x+(-9x)-1*108x^2=0

Wy multiply elements

-108x^2+12x+(-9x)=0

We get rid of parentheses

-108x^2+12x-9x=0

We add all the numbers together, and all the variables

-108x^2+3x=0

a = -108; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-108)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-108}=\frac{-6}{-216}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-108}=\frac{0}{-216}
=0
$