4x/x-8-2x/x-8=x/8

Solution for 4x/x-8-2x/x-8=x/8 equation:

4x/x-8-2x/x-8=x/8

We move all terms to the left:

4x/x-8-2x/x-8-(x/8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x/x-2x/x-(+x/8)-8-8=0

We add all the numbers together, and all the variables

4x/x-2x/x-(+x/8)-16=0

We get rid of parentheses

4x/x-2x/x-x/8-16=0

We calculate fractions


(-1x^2)/8x+(-12x)/8x-16=0

We multiply all the terms by the denominator


(-1x^2)+(-12x)-16*8x=0

Wy multiply elements

(-1x^2)+(-12x)-128x=0

We get rid of parentheses

-1x^2-12x-128x=0

We add all the numbers together, and all the variables

-1x^2-140x=0

a = -1; b = -140; c = 0;
Δ = b2-4ac
Δ = -1402-4·(-1)·0
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-140}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+140}{2*-1}=\frac{280}{-2}
=-140
$