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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

(-1x^2)/2x^2+16x/2x^2-7=0

We multiply all the terms by the denominator


(-1x^2)+16x-7*2x^2=0

Wy multiply elements

(-1x^2)-14x^2+16x=0

We get rid of parentheses

-1x^2-14x^2+16x=0

We add all the numbers together, and all the variables

-15x^2+16x=0

a = -15; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-15)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-15}=\frac{-32}{-30}
=1+1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-15}=\frac{0}{-30}
=0
$