x2/x+4=16/x+4

Solution for x2/x+4=16/x+4 equation:

x2/x+4=16/x+4

We move all terms to the left:

x2/x+4-(16/x+4)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

x2/x-16/x-4+4=0

We multiply all the terms by the denominator


x2-4*x+4*x-16=0

We add all the numbers together, and all the variables

x^2-16=0

a = 1; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·1·(-16)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*1}=\frac{8}{2}
=4
$