x/6=8x/x-5

Solution for x/6=8x/x-5 equation:

x/6=8x/x-5

We move all terms to the left:

x/6-(8x/x-5)=0


Domain of the equation: x-5)!=0

x∈R


We get rid of parentheses

x/6-8x/x+5=0

We calculate fractions


x^2/6x+(-48x)/6x+5=0

We multiply all the terms by the denominator


x^2+(-48x)+5*6x=0

Wy multiply elements

x^2+(-48x)+30x=0

We get rid of parentheses

x^2-48x+30x=0

We add all the numbers together, and all the variables

x^2-18x=0

a = 1; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·1·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*1}=\frac{36}{2}
=18
$