Y=2x-1/x+5

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

=2Y-1/Y+5

We move all terms to the left:

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


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

Y∈R


We get rid of parentheses

-2Y+1/Y-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -2; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-2)·1
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{33}}{2*-2}=\frac{5-\sqrt{33}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*-2}=\frac{5+\sqrt{33}}{-4}
$