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

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

=-(Y-6)(Y-2)

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1Y^2+8Y-12

Back to the equation:

-(-1Y^2+8Y-12)


We get rid of parentheses

1Y^2-8Y+12=0

We add all the numbers together, and all the variables

Y^2-8Y+12=0

a = 1; b = -8; c = +12;
Δ = b2-4ac
Δ = -82-4·1·12
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*1}=\frac{4}{2}
=2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*1}=\frac{12}{2}
=6
$