14+3x=49/x

Solution for 14+3x=49/x equation:

14+3x=49/x

We move all terms to the left:

14+3x-(49/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-(+49/x)+14=0

We get rid of parentheses

3x-49/x+14=0

We multiply all the terms by the denominator


3x*x+14*x-49=0

We add all the numbers together, and all the variables

14x+3x*x-49=0

Wy multiply elements

3x^2+14x-49=0

a = 3; b = 14; c = -49;
Δ = b2-4ac
Δ = 142-4·3·(-49)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-28}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+28}{2*3}=\frac{14}{6}
=2+1/3
$