Y=3(x-2)(x-6)

Solution for Y=3(x-2)(x-6) equation:

=3(Y-2)(Y-6)

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(3(+Y^2-6Y-2Y+12)), so:

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

We multiply parentheses

3Y^2-18Y-6Y+36

We add all the numbers together, and all the variables

3Y^2-24Y+36

Back to the equation:

-(3Y^2-24Y+36)


We get rid of parentheses

-3Y^2+24Y-36=0

a = -3; b = 24; c = -36;
Δ = b2-4ac
Δ = 242-4·(-3)·(-36)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*-3}=\frac{-36}{-6}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*-3}=\frac{-12}{-6}
=+2
$