Y=-3x^2+24x-36

Solution for Y=-3x^2+24x-36 equation:

=-3Y^2+24Y-36

We move all terms to the left:

-(-3Y^2+24Y-36)=0

We get rid of parentheses

3Y^2-24Y+36=0

a = 3; b = -24; c = +36;
Δ = b2-4ac
Δ = -242-4·3·36
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{-(-24)-12}{2*3}=\frac{12}{6}
=2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*3}=\frac{36}{6}
=6
$