15/08x-15/x=12

Solution for 15/08x-15/x=12 equation:

15/08x-15/x=12

We move all terms to the left:

15/08x-15/x-(12)=0


Domain of the equation: 08x!=0

x!=0/08

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


15x/8x^2+(-120x)/8x^2-12=0

We multiply all the terms by the denominator


15x+(-120x)-12*8x^2=0

Wy multiply elements

-96x^2+15x+(-120x)=0

We get rid of parentheses

-96x^2+15x-120x=0

We add all the numbers together, and all the variables

-96x^2-105x=0

a = -96; b = -105; c = 0;
Δ = b2-4ac
Δ = -1052-4·(-96)·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-105}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+105}{2*-96}=\frac{210}{-192}
=-1+3/32
$