X+x+1/4x=16

Solution for X+x+1/4x=16 equation:

X+X+1/4X=16

We move all terms to the left:

X+X+1/4X-(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

2X+1/4X-16=0

We multiply all the terms by the denominator


2X*4X-16*4X+1=0

Wy multiply elements

8X^2-64X+1=0

a = 8; b = -64; c = +1;
Δ = b2-4ac
Δ = -642-4·8·1
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*8}=\frac{64-4\sqrt{254}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{254}}{2*8}=\frac{64+4\sqrt{254}}{16}
$