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 calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

16x-12*(+0.8x*x)=0

We multiply parentheses

-0x^2+16x=0

We add all the numbers together, and all the variables

-1x^2+16x=0

a = -1; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-1)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-1}=\frac{-32}{-2}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-1}=\frac{0}{-2}
=0
$