4/x-8x=0

Solution for 4/x-8x=0 equation:

4/x-8x=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-8x+4/x=0

We multiply all the terms by the denominator


-8x*x+4=0

Wy multiply elements

-8x^2+4=0

a = -8; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-8)·4
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2}}{2*-8}=\frac{0-8\sqrt{2}}{-16}
=-\frac{8\sqrt{2}}{-16}
=-\frac{\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2}}{2*-8}=\frac{0+8\sqrt{2}}{-16}
=\frac{8\sqrt{2}}{-16}
=\frac{\sqrt{2}}{-2}
$