X+(1/4x)=8

Solution for X+(1/4x)=8 equation:

X+(1/4X)=8

We move all terms to the left:

X+(1/4X)-(8)=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+(+1/4X)-8=0

We get rid of parentheses

X+1/4X-8=0

We multiply all the terms by the denominator


X*4X-8*4X+1=0

Wy multiply elements

4X^2-32X+1=0

a = 4; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·4·1
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-12\sqrt{7}}{2*4}=\frac{32-12\sqrt{7}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+12\sqrt{7}}{2*4}=\frac{32+12\sqrt{7}}{8}
$