4x=128/x+2x

Solution for 4x=128/x+2x equation:

4x=128/x+2x

We move all terms to the left:

4x-(128/x+2x)=0


Domain of the equation: x+2x)!=0

x∈R


We add all the numbers together, and all the variables

4x-(+2x+128/x)=0

We get rid of parentheses

4x-2x-128/x=0

We multiply all the terms by the denominator


4x*x-2x*x-128=0

Wy multiply elements

4x^2-2x^2-128=0

We add all the numbers together, and all the variables

2x^2-128=0

a = 2; b = 0; c = -128;
Δ = b2-4ac
Δ = 02-4·2·(-128)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*2}=\frac{32}{4}
=8
$