Y=2x(x-3)

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

=2Y(Y-3)

We move all terms to the left:

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


We calculate terms in parentheses: -(2Y(Y-3)), so:

2Y(Y-3)

We multiply parentheses

2Y^2-6Y

Back to the equation:

-(2Y^2-6Y)


We get rid of parentheses

-2Y^2+6Y=0

a = -2; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-2)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-2}=\frac{-12}{-4}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-2}=\frac{0}{-4}
=0
$