Y=2(x-9)(x-4)

Solution for Y=2(x-9)(x-4) equation:

=2(Y-9)(Y-4)

We move all terms to the left:

-(2(Y-9)(Y-4))=0

We multiply parentheses ..

-(2(+Y^2-4Y-9Y+36))=0


We calculate terms in parentheses: -(2(+Y^2-4Y-9Y+36)), so:

2(+Y^2-4Y-9Y+36)

We multiply parentheses

2Y^2-8Y-18Y+72

We add all the numbers together, and all the variables

2Y^2-26Y+72

Back to the equation:

-(2Y^2-26Y+72)


We get rid of parentheses

-2Y^2+26Y-72=0

a = -2; b = 26; c = -72;
Δ = b2-4ac
Δ = 262-4·(-2)·(-72)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-10}{2*-2}=\frac{-36}{-4}
=+9
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+10}{2*-2}=\frac{-16}{-4}
=+4
$