y+1,000/2y=505

Solution for y+1,000/2y=505 equation:

y+1.000/2y=505

We move all terms to the left:

y+1.000/2y-(505)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


y*2y-505*2y+1.000=0

We add all the numbers together, and all the variables

y*2y-505*2y+1=0

Wy multiply elements

2y^2-1010y+1=0

a = 2; b = -1010; c = +1;
Δ = b2-4ac
Δ = -10102-4·2·1
Δ = 1020092
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1020092}=\sqrt{4*255023}=\sqrt{4}*\sqrt{255023}=2\sqrt{255023}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1010)-2\sqrt{255023}}{2*2}=\frac{1010-2\sqrt{255023}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1010)+2\sqrt{255023}}{2*2}=\frac{1010+2\sqrt{255023}}{4}
$