1/2x+x+x+1/2x=360

Solution for 1/2x+x+x+1/2x=360 equation:

1/2x+x+x+1/2x=360

We move all terms to the left:

1/2x+x+x+1/2x-(360)=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-360=0

We multiply all the terms by the denominator


2x*2x-360*2x+1+1=0

We add all the numbers together, and all the variables

2x*2x-360*2x+2=0

Wy multiply elements

4x^2-720x+2=0

a = 4; b = -720; c = +2;
Δ = b2-4ac
Δ = -7202-4·4·2
Δ = 518368
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:

$\sqrt{\Delta}=\sqrt{518368}=\sqrt{16*32398}=\sqrt{16}*\sqrt{32398}=4\sqrt{32398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32398}}{2*4}=\frac{720-4\sqrt{32398}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32398}}{2*4}=\frac{720+4\sqrt{32398}}{8}
$