16/x+4=x+28

Solution for 16/x+4=x+28 equation:

16/x+4=x+28

We move all terms to the left:

16/x+4-(x+28)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

16/x-x-28+4=0

We multiply all the terms by the denominator


-x*x-28*x+4*x+16=0

We add all the numbers together, and all the variables

-24x-x*x+16=0

Wy multiply elements

-1x^2-24x+16=0

a = -1; b = -24; c = +16;
Δ = b2-4ac
Δ = -242-4·(-1)·16
Δ = 640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{10}}{2*-1}=\frac{24-8\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{10}}{2*-1}=\frac{24+8\sqrt{10}}{-2}
$