0.5=x-20/x

Solution for 0.5=x-20/x equation:

0.5=x-20/x

We move all terms to the left:

0.5-(x-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)+0.5=0

We get rid of parentheses

-x+20/x+0.5=0

We multiply all the terms by the denominator


-x*x+(0.5)*x+20=0

We multiply parentheses

-x*x+0.5x+20=0

Wy multiply elements

-1x^2+0.5x+20=0

a = -1; b = 0.5; c = +20;
Δ = b2-4ac
Δ = 0.52-4·(-1)·20
Δ = 80.25
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{-(0.5)-\sqrt{80.25}}{2*-1}=\frac{-0.5-\sqrt{80.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{80.25}}{2*-1}=\frac{-0.5+\sqrt{80.25}}{-2}
$