x^2/x+14=32/x

Solution for x^2/x+14=32/x equation:

x^2/x+14=32/x

We move all terms to the left:

x^2/x+14-(32/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x^2/x-(+32/x)+14=0

We get rid of parentheses

x^2/x-32/x+14=0

We multiply all the terms by the denominator


x^2+14*x-32=0

We add all the numbers together, and all the variables

x^2+14x-32=0

a = 1; b = 14; c = -32;
Δ = b2-4ac
Δ = 142-4·1·(-32)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-18}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+18}{2*1}=\frac{4}{2}
=2
$