10x=5/4x

Solution for 10x=5/4x equation:

10x=5/4x

We move all terms to the left:

10x-(5/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10x-(+5/4x)=0

We get rid of parentheses

10x-5/4x=0

We multiply all the terms by the denominator


10x*4x-5=0

Wy multiply elements

40x^2-5=0

a = 40; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·40·(-5)
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*40}=\frac{0-20\sqrt{2}}{80}
=-\frac{20\sqrt{2}}{80}
=-\frac{\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*40}=\frac{0+20\sqrt{2}}{80}
=\frac{20\sqrt{2}}{80}
=\frac{\sqrt{2}}{4}
$