1.5x=300,000/x

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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} $

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