10/x-8=10/4x

Solution for 10/x-8=10/4x equation:

10/x-8=10/4x

We move all terms to the left:

10/x-8-(10/4x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10/x-(+10/4x)-8=0

We get rid of parentheses

10/x-10/4x-8=0

We calculate fractions


40x/4x^2+(-10x)/4x^2-8=0

We multiply all the terms by the denominator


40x+(-10x)-8*4x^2=0

Wy multiply elements

-32x^2+40x+(-10x)=0

We get rid of parentheses

-32x^2+40x-10x=0

We add all the numbers together, and all the variables

-32x^2+30x=0

a = -32; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-32)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-32}=\frac{-60}{-64}
=15/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-32}=\frac{0}{-64}
=0
$