X^=201/4x

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Solution for X^=201/4x equation: 



X^=201/4X

We move all terms to the left:

X^-(201/4X)=0



Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R



We add all the numbers together, and all the variables

X^-(+201/4X)=0

We add all the numbers together, and all the variables

X-(+201/4X)=0

We get rid of parentheses

X-201/4X=0

We multiply all the terms by the denominator


X*4X-201=0

Wy multiply elements

4X^2-201=0

a = 4; b = 0; c = -201;
Δ = b2-4ac
Δ = 02-4·4·(-201)
Δ = 3216
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:


$\sqrt{\Delta}=\sqrt{3216}=\sqrt{16*201}=\sqrt{16}*\sqrt{201}=4\sqrt{201}$


$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{201}}{2*4}=\frac{0-4\sqrt{201}}{8}
=-\frac{4\sqrt{201}}{8}
=-\frac{\sqrt{201}}{2}
$


$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{201}}{2*4}=\frac{0+4\sqrt{201}}{8}
=\frac{4\sqrt{201}}{8}
=\frac{\sqrt{201}}{2}
$

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