Y=x-12/x+6

Solution for Y=x-12/x+6 equation:

=Y-12/Y+6

We move all terms to the left:

-(Y-12/Y+6)=0


Domain of the equation: Y+6)!=0

Y∈R


We get rid of parentheses

-Y+12/Y-6=0

We multiply all the terms by the denominator


-Y*Y-6*Y+12=0

We add all the numbers together, and all the variables

-6Y-Y*Y+12=0

Wy multiply elements

-1Y^2-6Y+12=0

a = -1; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·(-1)·12
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*-1}=\frac{6-2\sqrt{21}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*-1}=\frac{6+2\sqrt{21}}{-2}
$