4/x+4/8x=8/40

Solution for 4/x+4/8x=8/40 equation:

4/x+4/8x=8/40

We move all terms to the left:

4/x+4/8x-(8/40)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

4/x+4/8x-(+8/40)=0

We get rid of parentheses

4/x+4/8x-8/40=0

We calculate fractions


(-512x^2)/1280x^2+5120x/1280x^2+640x/1280x^2=0

We multiply all the terms by the denominator


(-512x^2)+5120x+640x=0

We add all the numbers together, and all the variables

(-512x^2)+5760x=0

We get rid of parentheses

-512x^2+5760x=0

a = -512; b = 5760; c = 0;
Δ = b2-4ac
Δ = 57602-4·(-512)·0
Δ = 33177600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33177600}=5760$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5760)-5760}{2*-512}=\frac{-11520}{-1024}
=11+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5760)+5760}{2*-512}=\frac{0}{-1024}
=0
$