x+16=127.5/x

Solution for x+16=127.5/x equation:

x+16=127.5/x

We move all terms to the left:

x+16-(127.5/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+127.5/x)+16=0

We get rid of parentheses

x-127.5/x+16=0

We multiply all the terms by the denominator


x*x+16*x-127.5=0

We add all the numbers together, and all the variables

16x+x*x-127.5=0

Wy multiply elements

x^2+16x-127.5=0

a = 1; b = 16; c = -127.5;
Δ = b2-4ac
Δ = 162-4·1·(-127.5)
Δ = 766
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-\sqrt{766}}{2*1}=\frac{-16-\sqrt{766}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+\sqrt{766}}{2*1}=\frac{-16+\sqrt{766}}{2}
$