(4/x)+0.5x=5

Solution for (4/x)+0.5x=5 equation:

(4/x)+0.5x=5

We move all terms to the left:

(4/x)+0.5x-(5)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/x)+0.5x-5=0

We add all the numbers together, and all the variables

0.5x+(+4/x)-5=0

We get rid of parentheses

0.5x+4/x-5=0

We multiply all the terms by the denominator


(0.5x)*x-5*x+4=0

We add all the numbers together, and all the variables

(+0.5x)*x-5*x+4=0

We add all the numbers together, and all the variables

-5x+(+0.5x)*x+4=0

We multiply parentheses

0x^2-5x+4=0

We add all the numbers together, and all the variables

x^2-5x+4=0

a = 1; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·1·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*1}=\frac{8}{2}
=4
$