5=20-x-x(20-x)/x

Solution for 5=20-x-x(20-x)/x equation:

5=20-x-x(20-x)/x

We move all terms to the left:

5-(20-x-x(20-x)/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

-(20-x-x(-1x+20)/x)+5=0

We multiply all the terms by the denominator


-(20-x-x(-1x+20)+5*x)=0


We calculate terms in parentheses: -(20-x-x(-1x+20)+5*x), so:

20-x-x(-1x+20)+5*x

determiningTheFunctionDomain
-x-x(-1x+20)+5*x+20

We add all the numbers together, and all the variables

4x-x(-1x+20)+20

We multiply parentheses

1x^2+4x-20x+20

We add all the numbers together, and all the variables

x^2-16x+20

Back to the equation:

-(x^2-16x+20)


We get rid of parentheses

-x^2+16x-20=0

We add all the numbers together, and all the variables

-1x^2+16x-20=0

a = -1; b = 16; c = -20;
Δ = b2-4ac
Δ = 162-4·(-1)·(-20)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{11}}{2*-1}=\frac{-16-4\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{11}}{2*-1}=\frac{-16+4\sqrt{11}}{-2}
$