x+1/2x=360

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

x+1/2x=360

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-720x+1=0

a = 2; b = -720; c = +1;
Δ = b2-4ac
Δ = -7202-4·2·1
Δ = 518392
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:

$\sqrt{\Delta}=\sqrt{518392}=\sqrt{4*129598}=\sqrt{4}*\sqrt{129598}=2\sqrt{129598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-2\sqrt{129598}}{2*2}=\frac{720-2\sqrt{129598}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+2\sqrt{129598}}{2*2}=\frac{720+2\sqrt{129598}}{4}
$