16.2=x+1/2x

Solution for 16.2=x+1/2x equation:

16.2=x+1/2x

We move all terms to the left:

16.2-(x+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+1/2x)+16.2=0

We get rid of parentheses

-x-1/2x+16.2=0

We multiply all the terms by the denominator


-x*2x+(16.2)*2x-1=0

We multiply parentheses

-x*2x+32.4x-1=0

Wy multiply elements

-2x^2+32.4x-1=0

a = -2; b = 32.4; c = -1;
Δ = b2-4ac
Δ = 32.42-4·(-2)·(-1)
Δ = 1041.76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32.4)-\sqrt{1041.76}}{2*-2}=\frac{-32.4-\sqrt{1041.76}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32.4)+\sqrt{1041.76}}{2*-2}=\frac{-32.4+\sqrt{1041.76}}{-4}
$