100/x=x+16

Solution for 100/x=x+16 equation:

100/x=x+16

We move all terms to the left:

100/x-(x+16)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

100/x-x-16=0

We multiply all the terms by the denominator


-x*x-16*x+100=0

We add all the numbers together, and all the variables

-16x-x*x+100=0

Wy multiply elements

-1x^2-16x+100=0

a = -1; b = -16; c = +100;
Δ = b2-4ac
Δ = -162-4·(-1)·100
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{41}}{2*-1}=\frac{16-4\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{41}}{2*-1}=\frac{16+4\sqrt{41}}{-2}
$