(5/x)=x-4

Solution for (5/x)=x-4 equation:

(5/x)=x-4

We move all terms to the left:

(5/x)-(x-4)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/x)-(x-4)=0

We get rid of parentheses

5/x-x+4=0

We multiply all the terms by the denominator


-x*x+4*x+5=0

We add all the numbers together, and all the variables

4x-x*x+5=0

Wy multiply elements

-1x^2+4x+5=0

a = -1; b = 4; c = +5;
Δ = b2-4ac
Δ = 42-4·(-1)·5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6}{2*-1}=\frac{2}{-2}
=-1
$