3x+14=5/x

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

3x+14=5/x

We move all terms to the left:

3x+14-(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)+14=0

We get rid of parentheses

3x-5/x+14=0

We multiply all the terms by the denominator


3x*x+14*x-5=0

We add all the numbers together, and all the variables

14x+3x*x-5=0

Wy multiply elements

3x^2+14x-5=0

a = 3; b = 14; c = -5;
Δ = b2-4ac
Δ = 142-4·3·(-5)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-16}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+16}{2*3}=\frac{2}{6}
=1/3
$