1008x=500/x

Solution for 1008x=500/x equation:

1008x=500/x

We move all terms to the left:

1008x-(500/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1008x-(+500/x)=0

We get rid of parentheses

1008x-500/x=0

We multiply all the terms by the denominator


1008x*x-500=0

Wy multiply elements

1008x^2-500=0

a = 1008; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·1008·(-500)
Δ = 2016000
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:

$\sqrt{\Delta}=\sqrt{2016000}=\sqrt{57600*35}=\sqrt{57600}*\sqrt{35}=240\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-240\sqrt{35}}{2*1008}=\frac{0-240\sqrt{35}}{2016}
=-\frac{240\sqrt{35}}{2016}
=-\frac{5\sqrt{35}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+240\sqrt{35}}{2*1008}=\frac{0+240\sqrt{35}}{2016}
=\frac{240\sqrt{35}}{2016}
=\frac{5\sqrt{35}}{42}
$