Y=-3x2-24x+2

Solution for Y=-3x2-24x+2 equation:

=-3Y^2-24Y+2

We move all terms to the left:

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

We get rid of parentheses

3Y^2+24Y-2=0

a = 3; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·3·(-2)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*3}=\frac{-24-10\sqrt{6}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*3}=\frac{-24+10\sqrt{6}}{6}
$