Y=4x-12/x-2

Solution for Y=4x-12/x-2 equation:

=4Y-12/Y-2

We move all terms to the left:

-(4Y-12/Y-2)=0


Domain of the equation: Y-2)!=0

Y∈R


We get rid of parentheses

-4Y+12/Y+2=0

We multiply all the terms by the denominator


-4Y*Y+2*Y+12=0

We add all the numbers together, and all the variables

2Y-4Y*Y+12=0

Wy multiply elements

-4Y^2+2Y+12=0

a = -4; b = 2; c = +12;
Δ = b2-4ac
Δ = 22-4·(-4)·12
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*-4}=\frac{-16}{-8}
=+2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*-4}=\frac{12}{-8}
=-1+1/2
$