150x=10000/x

Solution for 150x=10000/x equation:

150x=10000/x

We move all terms to the left:

150x-(10000/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

150x-(+10000/x)=0

We get rid of parentheses

150x-10000/x=0

We multiply all the terms by the denominator


150x*x-10000=0

Wy multiply elements

150x^2-10000=0

a = 150; b = 0; c = -10000;
Δ = b2-4ac
Δ = 02-4·150·(-10000)
Δ = 6000000
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:

$\sqrt{\Delta}=\sqrt{6000000}=\sqrt{1000000*6}=\sqrt{1000000}*\sqrt{6}=1000\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1000\sqrt{6}}{2*150}=\frac{0-1000\sqrt{6}}{300}
=-\frac{1000\sqrt{6}}{300}
=-\frac{10\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1000\sqrt{6}}{2*150}=\frac{0+1000\sqrt{6}}{300}
=\frac{1000\sqrt{6}}{300}
=\frac{10\sqrt{6}}{3}
$