x+1/4x=185

Solution for x+1/4x=185 equation:

x+1/4x=185

We move all terms to the left:

x+1/4x-(185)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-185*4x+1=0

Wy multiply elements

4x^2-740x+1=0

a = 4; b = -740; c = +1;
Δ = b2-4ac
Δ = -7402-4·4·1
Δ = 547584
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:

$\sqrt{\Delta}=\sqrt{547584}=\sqrt{256*2139}=\sqrt{256}*\sqrt{2139}=16\sqrt{2139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-740)-16\sqrt{2139}}{2*4}=\frac{740-16\sqrt{2139}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-740)+16\sqrt{2139}}{2*4}=\frac{740+16\sqrt{2139}}{8}
$