x+41/4x=8

Solution for x+41/4x=8 equation:

x+41/4x=8

We move all terms to the left:

x+41/4x-(8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-8*4x+41=0

Wy multiply elements

4x^2-32x+41=0

a = 4; b = -32; c = +41;
Δ = b2-4ac
Δ = -322-4·4·41
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{23}}{2*4}=\frac{32-4\sqrt{23}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{23}}{2*4}=\frac{32+4\sqrt{23}}{8}
$