x=1500/5x

Solution for x=1500/5x equation:

x=1500/5x

We move all terms to the left:

x-(1500/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1500/5x)=0

We get rid of parentheses

x-1500/5x=0

We multiply all the terms by the denominator


x*5x-1500=0

Wy multiply elements

5x^2-1500=0

a = 5; b = 0; c = -1500;
Δ = b2-4ac
Δ = 02-4·5·(-1500)
Δ = 30000
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:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{3}}{2*5}=\frac{0-100\sqrt{3}}{10}
=-\frac{100\sqrt{3}}{10}
=-10\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{3}}{2*5}=\frac{0+100\sqrt{3}}{10}
=\frac{100\sqrt{3}}{10}
=10\sqrt{3}
$