5/x-1/2x=6

Solution for 5/x-1/2x=6 equation:

5/x-1/2x=6

We move all terms to the left:

5/x-1/2x-(6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


10x/2x^2+(-x)/2x^2-6=0

We add all the numbers together, and all the variables

10x/2x^2+(-1x)/2x^2-6=0

We multiply all the terms by the denominator


10x+(-1x)-6*2x^2=0

Wy multiply elements

-12x^2+10x+(-1x)=0

We get rid of parentheses

-12x^2+10x-1x=0

We add all the numbers together, and all the variables

-12x^2+9x=0

a = -12; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-12)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-12}=\frac{-18}{-24}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-12}=\frac{0}{-24}
=0
$