5/4x=2x

Solution for 5/4x=2x equation:

5/4x=2x

We move all terms to the left:

5/4x-(2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+5/4x=0

We multiply all the terms by the denominator


-2x*4x+5=0

Wy multiply elements

-8x^2+5=0

a = -8; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-8)·5
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*-8}=\frac{0-4\sqrt{10}}{-16}
=-\frac{4\sqrt{10}}{-16}
=-\frac{\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*-8}=\frac{0+4\sqrt{10}}{-16}
=\frac{4\sqrt{10}}{-16}
=\frac{\sqrt{10}}{-4}
$