x-1/4x=150

Solution for x-1/4x=150 equation:

x-1/4x=150

We move all terms to the left:

x-1/4x-(150)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-150*4x-1=0

Wy multiply elements

4x^2-600x-1=0

a = 4; b = -600; c = -1;
Δ = b2-4ac
Δ = -6002-4·4·(-1)
Δ = 360016
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:

$\sqrt{\Delta}=\sqrt{360016}=\sqrt{16*22501}=\sqrt{16}*\sqrt{22501}=4\sqrt{22501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-4\sqrt{22501}}{2*4}=\frac{600-4\sqrt{22501}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+4\sqrt{22501}}{2*4}=\frac{600+4\sqrt{22501}}{8}
$