Y=-3x^2+24x-45

Solution for Y=-3x^2+24x-45 equation:

=-3Y^2+24Y-45

We move all terms to the left:

-(-3Y^2+24Y-45)=0

We get rid of parentheses

3Y^2-24Y+45=0

a = 3; b = -24; c = +45;
Δ = b2-4ac
Δ = -242-4·3·45
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{-(-24)-6}{2*3}=\frac{18}{6}
=3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6}{2*3}=\frac{30}{6}
=5
$