1/5x-1/9x=12

Solution for 1/5x-1/9x=12 equation:

1/5x-1/9x=12

We move all terms to the left:

1/5x-1/9x-(12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We calculate fractions


9x/45x^2+(-5x)/45x^2-12=0

We multiply all the terms by the denominator


9x+(-5x)-12*45x^2=0

Wy multiply elements

-540x^2+9x+(-5x)=0

We get rid of parentheses

-540x^2+9x-5x=0

We add all the numbers together, and all the variables

-540x^2+4x=0

a = -540; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-540)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-540}=\frac{-8}{-1080}
=1/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-540}=\frac{0}{-1080}
=0
$