3x+2=14/x=4

Solution for 3x+2=14/x=4 equation:

3x+2=14/x=4

We move all terms to the left:

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

We get rid of parentheses

3x-14/x+2=0

We multiply all the terms by the denominator


3x*x+2*x-14=0

We add all the numbers together, and all the variables

2x+3x*x-14=0

Wy multiply elements

3x^2+2x-14=0

a = 3; b = 2; c = -14;
Δ = b2-4ac
Δ = 22-4·3·(-14)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{43}}{2*3}=\frac{-2-2\sqrt{43}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{43}}{2*3}=\frac{-2+2\sqrt{43}}{6}
$