Y=x-1/x+5

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

=Y-1/Y+5

We move all terms to the left:

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


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

Y∈R


We get rid of parentheses

-Y+1/Y-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-5Y-Y*Y+1=0

Wy multiply elements

-1Y^2-5Y+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:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{29}}{2*-1}=\frac{5-\sqrt{29}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{29}}{2*-1}=\frac{5+\sqrt{29}}{-2}
$