1/x-8=x/2x-16

Solution for 1/x-8=x/2x-16 equation:

1/x-8=x/2x-16

We move all terms to the left:

1/x-8-(x/2x-16)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-16)!=0

x∈R


We get rid of parentheses

1/x-x/2x+16-8=0

We calculate fractions


(-1x^2)/2x^2+2x/2x^2+16-8=0

We add all the numbers together, and all the variables

(-1x^2)/2x^2+2x/2x^2+8=0

We multiply all the terms by the denominator


(-1x^2)+2x+8*2x^2=0

Wy multiply elements

(-1x^2)+16x^2+2x=0

We get rid of parentheses

-1x^2+16x^2+2x=0

We add all the numbers together, and all the variables

15x^2+2x=0

a = 15; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·15·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*15}=\frac{-4}{30}
=-2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*15}=\frac{0}{30}
=0
$