2x+x+1/2x=84

Solution for 2x+x+1/2x=84 equation:

2x+x+1/2x=84

We move all terms to the left:

2x+x+1/2x-(84)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-84=0

We multiply all the terms by the denominator


3x*2x-84*2x+1=0

Wy multiply elements

6x^2-168x+1=0

a = 6; b = -168; c = +1;
Δ = b2-4ac
Δ = -1682-4·6·1
Δ = 28200
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:

$\sqrt{\Delta}=\sqrt{28200}=\sqrt{100*282}=\sqrt{100}*\sqrt{282}=10\sqrt{282}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-10\sqrt{282}}{2*6}=\frac{168-10\sqrt{282}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+10\sqrt{282}}{2*6}=\frac{168+10\sqrt{282}}{12}
$