X+1/4x=128

Solution for X+1/4x=128 equation:

X+1/4X=128

We move all terms to the left:

X+1/4X-(128)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-128*4X+1=0

Wy multiply elements

4X^2-512X+1=0

a = 4; b = -512; c = +1;
Δ = b2-4ac
Δ = -5122-4·4·1
Δ = 262128
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:

$\sqrt{\Delta}=\sqrt{262128}=\sqrt{16*16383}=\sqrt{16}*\sqrt{16383}=4\sqrt{16383}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-512)-4\sqrt{16383}}{2*4}=\frac{512-4\sqrt{16383}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-512)+4\sqrt{16383}}{2*4}=\frac{512+4\sqrt{16383}}{8}
$