Y=-x(x-3)

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

=-Y(Y-3)

We move all terms to the left:

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


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

-Y(Y-3)

We multiply parentheses

-Y^2+3Y

We add all the numbers together, and all the variables

-1Y^2+3Y

Back to the equation:

-(-1Y^2+3Y)


We get rid of parentheses

1Y^2-3Y=0

We add all the numbers together, and all the variables

Y^2-3Y=0

a = 1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·1·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*1}=\frac{0}{2}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*1}=\frac{6}{2}
=3
$