5x+1/3x=5

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Solution for 5x+1/3x=5 equation: 



5x+1/3x=5

We move all terms to the left:

5x+1/3x-(5)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We multiply all the terms by the denominator


5x*3x-5*3x+1=0

Wy multiply elements

15x^2-15x+1=0

a = 15; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·15·1
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{165}}{2*15}=\frac{15-\sqrt{165}}{30}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{165}}{2*15}=\frac{15+\sqrt{165}}{30}
$

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