x+1/2x=5000

Solution for x+1/2x=5000 equation:

x+1/2x=5000

We move all terms to the left:

x+1/2x-(5000)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-5000*2x+1=0

Wy multiply elements

2x^2-10000x+1=0

a = 2; b = -10000; c = +1;
Δ = b2-4ac
Δ = -100002-4·2·1
Δ = 99999992
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:

$\sqrt{\Delta}=\sqrt{99999992}=\sqrt{4*24999998}=\sqrt{4}*\sqrt{24999998}=2\sqrt{24999998}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10000)-2\sqrt{24999998}}{2*2}=\frac{10000-2\sqrt{24999998}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10000)+2\sqrt{24999998}}{2*2}=\frac{10000+2\sqrt{24999998}}{4}
$