x-1/4x=129

Solution for x-1/4x=129 equation:

x-1/4x=129

We move all terms to the left:

x-1/4x-(129)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-129*4x-1=0

Wy multiply elements

4x^2-516x-1=0

a = 4; b = -516; c = -1;
Δ = b2-4ac
Δ = -5162-4·4·(-1)
Δ = 266272
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:

$\sqrt{\Delta}=\sqrt{266272}=\sqrt{16*16642}=\sqrt{16}*\sqrt{16642}=4\sqrt{16642}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-516)-4\sqrt{16642}}{2*4}=\frac{516-4\sqrt{16642}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-516)+4\sqrt{16642}}{2*4}=\frac{516+4\sqrt{16642}}{8}
$