1/2x+x=16.2

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

1/2x+x=16.2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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}
$