(3x)+(5/3x)=90

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Solution for (3x)+(5/3x)=90 equation:



(3x)+(5/3x)=90
We move all terms to the left:
(3x)+(5/3x)-(90)=0
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
3x+(+5/3x)-90=0
We get rid of parentheses
3x+5/3x-90=0
We multiply all the terms by the denominator
3x*3x-90*3x+5=0
Wy multiply elements
9x^2-270x+5=0
a = 9; b = -270; c = +5;
Δ = b2-4ac
Δ = -2702-4·9·5
Δ = 72720
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:
$\sqrt{\Delta}=\sqrt{72720}=\sqrt{144*505}=\sqrt{144}*\sqrt{505}=12\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-12\sqrt{505}}{2*9}=\frac{270-12\sqrt{505}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+12\sqrt{505}}{2*9}=\frac{270+12\sqrt{505}}{18} $

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