Y=3x^2-9x-30

Solution for Y=3x^2-9x-30 equation:

=3Y^2-9Y-30

We move all terms to the left:

-(3Y^2-9Y-30)=0

We get rid of parentheses

-3Y^2+9Y+30=0

a = -3; b = 9; c = +30;
Δ = b2-4ac
Δ = 92-4·(-3)·30
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*-3}=\frac{-30}{-6}
=+5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*-3}=\frac{12}{-6}
=-2
$