1000/x=10x

Solution for 1000/x=10x equation:

1000/x=10x

We move all terms to the left:

1000/x-(10x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-10x+1000/x=0

We multiply all the terms by the denominator


-10x*x+1000=0

Wy multiply elements

-10x^2+1000=0

a = -10; b = 0; c = +1000;
Δ = b2-4ac
Δ = 02-4·(-10)·1000
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200}{2*-10}=\frac{-200}{-20}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200}{2*-10}=\frac{200}{-20}
=-10
$