Y=-(x-2)(x+4)

Solution for Y=-(x-2)(x+4) equation:

=-(Y-2)(Y+4)

We move all terms to the left:

-(-(Y-2)(Y+4))=0

We multiply parentheses ..

-(-(+Y^2+4Y-2Y-8))=0


We calculate terms in parentheses: -(-(+Y^2+4Y-2Y-8)), so:

-(+Y^2+4Y-2Y-8)

We get rid of parentheses

-Y^2-4Y+2Y+8

We add all the numbers together, and all the variables

-1Y^2-2Y+8

Back to the equation:

-(-1Y^2-2Y+8)


We get rid of parentheses

1Y^2+2Y-8=0

We add all the numbers together, and all the variables

Y^2+2Y-8=0

a = 1; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·1·(-8)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*1}=\frac{-8}{2}
=-4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*1}=\frac{4}{2}
=2
$