Y=2x-1/x-3

Solution for Y=2x-1/x-3 equation:

=2Y-1/Y-3

We move all terms to the left:

-(2Y-1/Y-3)=0


Domain of the equation: Y-3)!=0

Y∈R


We get rid of parentheses

-2Y+1/Y+3=0

We multiply all the terms by the denominator


-2Y*Y+3*Y+1=0

We add all the numbers together, and all the variables

3Y-2Y*Y+1=0

Wy multiply elements

-2Y^2+3Y+1=0

a = -2; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-2)·1
Δ = 17
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{-(3)-\sqrt{17}}{2*-2}=\frac{-3-\sqrt{17}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{17}}{2*-2}=\frac{-3+\sqrt{17}}{-4}
$