1/2x+x+x1/2x=360

Solution for 1/2x+x+x1/2x=360 equation:

1/2x+x+x1/2x=360

We move all terms to the left:

1/2x+x+x1/2x-(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

x+1/2x+x1/2x-360=0

We multiply all the terms by the denominator


x*2x+x1-360*2x+1=0

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2+x-720x+1=0

We add all the numbers together, and all the variables

2x^2-719x+1=0

a = 2; b = -719; c = +1;
Δ = b2-4ac
Δ = -7192-4·2·1
Δ = 516953
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{-(-719)-\sqrt{516953}}{2*2}=\frac{719-\sqrt{516953}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-719)+\sqrt{516953}}{2*2}=\frac{719+\sqrt{516953}}{4}
$