(5x=1)/x=4.5

Solution for (5x=1)/x=4.5 equation:

(5x=1)/x=4.5

We move all terms to the left:

(5x-(1)/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

(+5x-1/x)=0

We get rid of parentheses

5x-1/x=0

We multiply all the terms by the denominator


5x*x-1=0

Wy multiply elements

5x^2-1=0

a = 5; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·5·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*5}=\frac{0-2\sqrt{5}}{10}
=-\frac{2\sqrt{5}}{10}
=-\frac{\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*5}=\frac{0+2\sqrt{5}}{10}
=\frac{2\sqrt{5}}{10}
=\frac{\sqrt{5}}{5}
$