400x=15/4x

Solution for 400x=15/4x equation:

400x=15/4x

We move all terms to the left:

400x-(15/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

400x-(+15/4x)=0

We get rid of parentheses

400x-15/4x=0

We multiply all the terms by the denominator


400x*4x-15=0

Wy multiply elements

1600x^2-15=0

a = 1600; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·1600·(-15)
Δ = 96000
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:

$\sqrt{\Delta}=\sqrt{96000}=\sqrt{6400*15}=\sqrt{6400}*\sqrt{15}=80\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{15}}{2*1600}=\frac{0-80\sqrt{15}}{3200}
=-\frac{80\sqrt{15}}{3200}
=-\frac{\sqrt{15}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{15}}{2*1600}=\frac{0+80\sqrt{15}}{3200}
=\frac{80\sqrt{15}}{3200}
=\frac{\sqrt{15}}{40}
$