x-1/4x=168

Solution for x-1/4x=168 equation:

x-1/4x=168

We move all terms to the left:

x-1/4x-(168)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-168*4x-1=0

Wy multiply elements

4x^2-672x-1=0

a = 4; b = -672; c = -1;
Δ = b2-4ac
Δ = -6722-4·4·(-1)
Δ = 451600
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:

$\sqrt{\Delta}=\sqrt{451600}=\sqrt{400*1129}=\sqrt{400}*\sqrt{1129}=20\sqrt{1129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-20\sqrt{1129}}{2*4}=\frac{672-20\sqrt{1129}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+20\sqrt{1129}}{2*4}=\frac{672+20\sqrt{1129}}{8}
$