3x+(8/x)=14

Solution for 3x+(8/x)=14 equation:

3x+(8/x)=14

We move all terms to the left:

3x+(8/x)-(14)=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+(+8/x)-14=0

We get rid of parentheses

3x+8/x-14=0

We multiply all the terms by the denominator


3x*x-14*x+8=0

We add all the numbers together, and all the variables

-14x+3x*x+8=0

Wy multiply elements

3x^2-14x+8=0

a = 3; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·3·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*3}=\frac{4}{6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*3}=\frac{24}{6}
=4
$