15/(0.8x)-15/x=12

Solution for 15/(0.8x)-15/x=12 equation:

15/(0.8x)-15/x=12

We move all terms to the left:

15/(0.8x)-15/x-(12)=0


Domain of the equation: (0.8x)!=0

x!=0/0.8

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

15/(+0.8x)-15/x-12=0

We calculate fractions


15x/x^2+(-x)/x^2-12=0

We add all the numbers together, and all the variables

15x/x^2+(-1x)/x^2-12=0

We multiply all the terms by the denominator


15x+(-1x)-12*x^2=0

We add all the numbers together, and all the variables

-12x^2+15x+(-1x)=0

We get rid of parentheses

-12x^2+15x-1x=0

We add all the numbers together, and all the variables

-12x^2+14x=0

a = -12; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-12)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-12}=\frac{-28}{-24}
=1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-12}=\frac{0}{-24}
=0
$