Y=3x(x-4)

Solution for Y=3x(x-4) equation:

=3Y(Y-4)

We move all terms to the left:

-(3Y(Y-4))=0


We calculate terms in parentheses: -(3Y(Y-4)), so:

3Y(Y-4)

We multiply parentheses

3Y^2-12Y

Back to the equation:

-(3Y^2-12Y)


We get rid of parentheses

-3Y^2+12Y=0

a = -3; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-3)·0
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{-(12)-12}{2*-3}=\frac{-24}{-6}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-3}=\frac{0}{-6}
=0
$