x+16=20/x=4

Solution for x+16=20/x=4 equation:

x+16=20/x=4

We move all terms to the left:

x+16-(20/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-(+20/x)+16=0

We get rid of parentheses

x-20/x+16=0

We multiply all the terms by the denominator


x*x+16*x-20=0

We add all the numbers together, and all the variables

16x+x*x-20=0

Wy multiply elements

x^2+16x-20=0

a = 1; b = 16; c = -20;
Δ = b2-4ac
Δ = 162-4·1·(-20)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{21}}{2*1}=\frac{-16-4\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{21}}{2*1}=\frac{-16+4\sqrt{21}}{2}
$