1/2x+2*x=18

Solution for 1/2x+2*x=18 equation:

1/2x+2x=18

We move all terms to the left:

1/2x+2x-(18)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x-18=0

We multiply all the terms by the denominator


2x*2x-18*2x+1=0

Wy multiply elements

4x^2-36x+1=0

a = 4; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·4·1
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-16\sqrt{5}}{2*4}=\frac{36-16\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+16\sqrt{5}}{2*4}=\frac{36+16\sqrt{5}}{8}
$