(x)=2x-1/x+5

Solution for (x)=2x-1/x+5 equation:

(x)=2x-1/x+5

We move all terms to the left:

(x)-(2x-1/x+5)=0


Domain of the equation: x+5)!=0

x∈R


We get rid of parentheses

x-2x+1/x-5=0

We multiply all the terms by the denominator


x*x-2x*x-5*x+1=0

We add all the numbers together, and all the variables

-5x+x*x-2x*x+1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -1; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-1)·1
Δ = 29
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{-(-5)-\sqrt{29}}{2*-1}=\frac{5-\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{29}}{2*-1}=\frac{5+\sqrt{29}}{-2}
$