Y=-2x(x-4.5)

Solution for Y=-2x(x-4.5) equation:

=-2Y(Y-4.5)

We move all terms to the left:

-(-2Y(Y-4.5))=0


We calculate terms in parentheses: -(-2Y(Y-4.5)), so:

-2Y(Y-4.5)

We multiply parentheses

-2Y^2+9Y

Back to the equation:

-(-2Y^2+9Y)


We get rid of parentheses

2Y^2-9Y=0

a = 2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·2·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*2}=\frac{0}{4}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*2}=\frac{18}{4}
=4+1/2
$