Y=(2-x)(x+6)

Solution for Y=(2-x)(x+6) equation:

=(2-Y)(Y+6)

We move all terms to the left:

-((2-Y)(Y+6))=0

We add all the numbers together, and all the variables

-((-1Y+2)(Y+6))=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((-1Y^2-6Y+2Y+12)), so:

(-1Y^2-6Y+2Y+12)

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1Y^2-4Y+12

Back to the equation:

-(-1Y^2-4Y+12)


We get rid of parentheses

1Y^2+4Y-12=0

We add all the numbers together, and all the variables

Y^2+4Y-12=0

a = 1; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·1·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*1}=\frac{-12}{2}
=-6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*1}=\frac{4}{2}
=2
$