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

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

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

We move all terms to the left:

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


Domain of the equation: x-4))!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x*x+4*x-4))-(1)=0

We add all the numbers together, and all the variables

4x+x*x=0

Wy multiply elements

x^2+4x=0

a = 1; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·1·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*1}=\frac{0}{2}
=0
$