1/2x+x=16.

Solution for 1/2x+x=16. equation:

1/2x+x=16.

We move all terms to the left:

1/2x+x-(16.)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+x-16=0

We add all the numbers together, and all the variables

x+1/2x-16=0

We multiply all the terms by the denominator


x*2x-16*2x+1=0

Wy multiply elements

2x^2-32x+1=0

a = 2; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·2·1
Δ = 1016
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:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{254}}{2*2}=\frac{32-2\sqrt{254}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{254}}{2*2}=\frac{32+2\sqrt{254}}{4}
$