Y=-3x^2-21x-30

Solution for Y=-3x^2-21x-30 equation:

=-3Y^2-21Y-30

We move all terms to the left:

-(-3Y^2-21Y-30)=0

We get rid of parentheses

3Y^2+21Y+30=0

a = 3; b = 21; c = +30;
Δ = b2-4ac
Δ = 212-4·3·30
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-9}{2*3}=\frac{-30}{6}
=-5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+9}{2*3}=\frac{-12}{6}
=-2
$