42/0.5x-42/x=1/6

Solution for 42/0.5x-42/x=1/6 equation:

42/0.5x-42/x=1/6

We move all terms to the left:

42/0.5x-42/x-(1/6)=0


Domain of the equation: 0.5x!=0

x!=0/0.5

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

42/0.5x-42/x-(+1/6)=0

We get rid of parentheses

42/0.5x-42/x-1/6=0

We calculate fractions


x^2/(0.5x*x*6)+1512x/(0.5x*x*6)+x/(0.5x*x*6)=0

We add all the numbers together, and all the variables

x^2/(+0.5x*x*6)+1512x/(+0.5x*x*6)+x/(+0.5x*x*6)=0

We multiply all the terms by the denominator


x^2+1512x+x=0

We add all the numbers together, and all the variables

x^2+1513x=0

a = 1; b = 1513; c = 0;
Δ = b2-4ac
Δ = 15132-4·1·0
Δ = 2289169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2289169}=1513$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1513)-1513}{2*1}=\frac{-3026}{2}
=-1513
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1513)+1513}{2*1}=\frac{0}{2}
=0
$