3x=5/x

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Solution for 3x=5/x equation:



3x=5/x
We move all terms to the left:
3x-(5/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
3x-(+5/x)=0
We get rid of parentheses
3x-5/x=0
We multiply all the terms by the denominator
3x*x-5=0
Wy multiply elements
3x^2-5=0
a = 3; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·3·(-5)
Δ = 60
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:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*3}=\frac{0-2\sqrt{15}}{6} =-\frac{2\sqrt{15}}{6} =-\frac{\sqrt{15}}{3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*3}=\frac{0+2\sqrt{15}}{6} =\frac{2\sqrt{15}}{6} =\frac{\sqrt{15}}{3} $

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