2/4x+x=16

Solution for 2/4x+x=16 equation:

2/4x+x=16

We move all terms to the left:

2/4x+x-(16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+2/4x-16=0

We multiply all the terms by the denominator


x*4x-16*4x+2=0

Wy multiply elements

4x^2-64x+2=0

a = 4; b = -64; c = +2;
Δ = b2-4ac
Δ = -642-4·4·2
Δ = 4064
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:

$\sqrt{\Delta}=\sqrt{4064}=\sqrt{16*254}=\sqrt{16}*\sqrt{254}=4\sqrt{254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{254}}{2*4}=\frac{64-4\sqrt{254}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{254}}{2*4}=\frac{64+4\sqrt{254}}{8}
$