Y=-3x^2+24x+52

Solution for Y=-3x^2+24x+52 equation:

=-3Y^2+24Y+52

We move all terms to the left:

-(-3Y^2+24Y+52)=0

We get rid of parentheses

3Y^2-24Y-52=0

a = 3; b = -24; c = -52;
Δ = b2-4ac
Δ = -242-4·3·(-52)
Δ = 1200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-20\sqrt{3}}{2*3}=\frac{24-20\sqrt{3}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+20\sqrt{3}}{2*3}=\frac{24+20\sqrt{3}}{6}
$