1.5x=300,000/x

Solution for 1.5x=300,000/x equation:

1.5x=300.000/x

We move all terms to the left:

1.5x-(300.000/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

1.5x-(+300.000/x)=0

We get rid of parentheses

1.5x-300.000/x=0

We multiply all the terms by the denominator


(1.5x)*x-300.000=0

We add all the numbers together, and all the variables

(+1.5x)*x-300.000=0

We add all the numbers together, and all the variables

(+1.5x)*x-300=0

We multiply parentheses

x^2-300=0

a = 1; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·1·(-300)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*1}=\frac{0-20\sqrt{3}}{2}
=-\frac{20\sqrt{3}}{2}
=-10\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*1}=\frac{0+20\sqrt{3}}{2}
=\frac{20\sqrt{3}}{2}
=10\sqrt{3}
$