1000+2x+5000/2x=0

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Solution for 1000+2x+5000/2x=0 equation: 



1000+2x+5000/2x=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We multiply all the terms by the denominator


2x*2x+1000*2x+5000=0

Wy multiply elements

4x^2+2000x+5000=0

a = 4; b = 2000; c = +5000;
Δ = b2-4ac
Δ = 20002-4·4·5000
Δ = 3920000
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:


$\sqrt{\Delta}=\sqrt{3920000}=\sqrt{1960000*2}=\sqrt{1960000}*\sqrt{2}=1400\sqrt{2}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2000)-1400\sqrt{2}}{2*4}=\frac{-2000-1400\sqrt{2}}{8}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2000)+1400\sqrt{2}}{2*4}=\frac{-2000+1400\sqrt{2}}{8}
$

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