5x/14x+3=1/x

Solution for 5x/14x+3=1/x equation:

5x/14x+3=1/x

We move all terms to the left:

5x/14x+3-(1/x)=0


Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x/14x-(+1/x)+3=0

We get rid of parentheses

5x/14x-1/x+3=0

We calculate fractions


5x^2/14x^2+(-14x)/14x^2+3=0

We multiply all the terms by the denominator


5x^2+(-14x)+3*14x^2=0

Wy multiply elements

5x^2+42x^2+(-14x)=0

We get rid of parentheses

5x^2+42x^2-14x=0

We add all the numbers together, and all the variables

47x^2-14x=0

a = 47; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·47·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*47}=\frac{0}{94}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*47}=\frac{28}{94}
=14/47
$