Y=2x-3/3x-1

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

=2Y-3/3Y-1

We move all terms to the left:

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


Domain of the equation: 3Y-1)!=0

Y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6Y^2+3Y+3=0

a = -6; b = 3; c = +3;
Δ = b2-4ac
Δ = 32-4·(-6)·3
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-6}=\frac{-12}{-12}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-6}=\frac{6}{-12}
=-1/2
$