5x=5+0.1/x

Solution for 5x=5+0.1/x equation:

5x=5+0.1/x

We move all terms to the left:

5x-(5+0.1/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-(0.1/x+5)=0

We get rid of parentheses

5x-0.1/x-5=0

We multiply all the terms by the denominator


5x*x-5*x-0.1=0

We add all the numbers together, and all the variables

-5x+5x*x-0.1=0

Wy multiply elements

5x^2-5x-0.1=0

a = 5; b = -5; c = -0.1;
Δ = b2-4ac
Δ = -52-4·5·(-0.1)
Δ = 27
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:

$\sqrt{\Delta}=\sqrt{27}=\sqrt{9*3}=\sqrt{9}*\sqrt{3}=3\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{3}}{2*5}=\frac{5-3\sqrt{3}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{3}}{2*5}=\frac{5+3\sqrt{3}}{10}
$