2x+5=14/x

Solution for 2x+5=14/x equation:

2x+5=14/x

We move all terms to the left:

2x+5-(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

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

We get rid of parentheses

2x-14/x+5=0

We multiply all the terms by the denominator


2x*x+5*x-14=0

We add all the numbers together, and all the variables

5x+2x*x-14=0

Wy multiply elements

2x^2+5x-14=0

a = 2; b = 5; c = -14;
Δ = b2-4ac
Δ = 52-4·2·(-14)
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{137}}{2*2}=\frac{-5-\sqrt{137}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{137}}{2*2}=\frac{-5+\sqrt{137}}{4}
$