Y=(3x-9)(6x-3)

Solution for Y=(3x-9)(6x-3) equation:

=(3Y-9)(6Y-3)

We move all terms to the left:

-((3Y-9)(6Y-3))=0

We multiply parentheses ..

-((+18Y^2-9Y-54Y+27))=0


We calculate terms in parentheses: -((+18Y^2-9Y-54Y+27)), so:

(+18Y^2-9Y-54Y+27)

We get rid of parentheses

18Y^2-9Y-54Y+27

We add all the numbers together, and all the variables

18Y^2-63Y+27

Back to the equation:

-(18Y^2-63Y+27)


We get rid of parentheses

-18Y^2+63Y-27=0

a = -18; b = 63; c = -27;
Δ = b2-4ac
Δ = 632-4·(-18)·(-27)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-45}{2*-18}=\frac{-108}{-36}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+45}{2*-18}=\frac{-18}{-36}
=1/2
$