4x=1/2x*5

Solution for 4x=1/2x*5 equation:

4x=1/2x*5

We move all terms to the left:

4x-(1/2x*5)=0


Domain of the equation: 2x*5)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+1/2x*5)=0

We get rid of parentheses

4x-1/2x*5=0

We multiply all the terms by the denominator


4x*2x*5-1=0

Wy multiply elements

40x^2*5-1=0

Wy multiply elements

200x^2-1=0

a = 200; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·200·(-1)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*200}=\frac{0-20\sqrt{2}}{400}
=-\frac{20\sqrt{2}}{400}
=-\frac{\sqrt{2}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*200}=\frac{0+20\sqrt{2}}{400}
=\frac{20\sqrt{2}}{400}
=\frac{\sqrt{2}}{20}
$