x-1/4x=186

Solution for x-1/4x=186 equation:

x-1/4x=186

We move all terms to the left:

x-1/4x-(186)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-186*4x-1=0

Wy multiply elements

4x^2-744x-1=0

a = 4; b = -744; c = -1;
Δ = b2-4ac
Δ = -7442-4·4·(-1)
Δ = 553552
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:

$\sqrt{\Delta}=\sqrt{553552}=\sqrt{16*34597}=\sqrt{16}*\sqrt{34597}=4\sqrt{34597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-744)-4\sqrt{34597}}{2*4}=\frac{744-4\sqrt{34597}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-744)+4\sqrt{34597}}{2*4}=\frac{744+4\sqrt{34597}}{8}
$