x=5x-1/x+3

Solution for x=5x-1/x+3 equation:

x=5x-1/x+3

We move all terms to the left:

x-(5x-1/x+3)=0


Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

x-5x+1/x-3=0

We multiply all the terms by the denominator


x*x-5x*x-3*x+1=0

We add all the numbers together, and all the variables

-3x+x*x-5x*x+1=0

Wy multiply elements

x^2-5x^2-3x+1=0

We add all the numbers together, and all the variables

-4x^2-3x+1=0

a = -4; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-4)·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*-4}=\frac{-2}{-8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*-4}=\frac{8}{-8}
=-1
$