1/2x+2+x+1/2x+2+x=40

Solution for 1/2x+2+x+1/2x+2+x=40 equation:

1/2x+2+x+1/2x+2+x=40

We move all terms to the left:

1/2x+2+x+1/2x+2+x-(40)=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+1/2x-36=0

We multiply all the terms by the denominator


2x*2x-36*2x+1+1=0

We add all the numbers together, and all the variables

2x*2x-36*2x+2=0

Wy multiply elements

4x^2-72x+2=0

a = 4; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·4·2
Δ = 5152
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:

$\sqrt{\Delta}=\sqrt{5152}=\sqrt{16*322}=\sqrt{16}*\sqrt{322}=4\sqrt{322}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{322}}{2*4}=\frac{72-4\sqrt{322}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{322}}{2*4}=\frac{72+4\sqrt{322}}{8}
$