x=1680/x

Solution for x=1680/x equation:

x=1680/x

We move all terms to the left:

x-(1680/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

x-(+1680/x)=0

We get rid of parentheses

x-1680/x=0

We multiply all the terms by the denominator


x*x-1680=0

Wy multiply elements

x^2-1680=0

a = 1; b = 0; c = -1680;
Δ = b2-4ac
Δ = 02-4·1·(-1680)
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{105}}{2*1}=\frac{0-8\sqrt{105}}{2}
=-\frac{8\sqrt{105}}{2}
=-4\sqrt{105}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{105}}{2*1}=\frac{0+8\sqrt{105}}{2}
=\frac{8\sqrt{105}}{2}
=4\sqrt{105}
$