x+14=72/x

Solution for x+14=72/x equation:

x+14=72/x

We move all terms to the left:

x+14-(72/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

x-(+72/x)+14=0

We get rid of parentheses

x-72/x+14=0

We multiply all the terms by the denominator


x*x+14*x-72=0

We add all the numbers together, and all the variables

14x+x*x-72=0

Wy multiply elements

x^2+14x-72=0

a = 1; b = 14; c = -72;
Δ = b2-4ac
Δ = 142-4·1·(-72)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-22}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+22}{2*1}=\frac{8}{2}
=4
$