Y=3x-4/x-3

Solution for Y=3x-4/x-3 equation:

=3Y-4/Y-3

We move all terms to the left:

-(3Y-4/Y-3)=0


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

Y∈R


We get rid of parentheses

-3Y+4/Y+3=0

We multiply all the terms by the denominator


-3Y*Y+3*Y+4=0

We add all the numbers together, and all the variables

3Y-3Y*Y+4=0

Wy multiply elements

-3Y^2+3Y+4=0

a = -3; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-3)·4
Δ = 57
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{57}}{2*-3}=\frac{-3-\sqrt{57}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*-3}=\frac{-3+\sqrt{57}}{-6}
$