-1+5x=10/x

Solution for -1+5x=10/x equation:

-1+5x=10/x

We move all terms to the left:

-1+5x-(10/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-(+10/x)-1=0

We get rid of parentheses

5x-10/x-1=0

We multiply all the terms by the denominator


5x*x-1*x-10=0

We add all the numbers together, and all the variables

-1x+5x*x-10=0

Wy multiply elements

5x^2-1x-10=0

a = 5; b = -1; c = -10;
Δ = b2-4ac
Δ = -12-4·5·(-10)
Δ = 201
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{-(-1)-\sqrt{201}}{2*5}=\frac{1-\sqrt{201}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{201}}{2*5}=\frac{1+\sqrt{201}}{10}
$