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

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

=-30+9Y+3Y^2

We move all terms to the left:

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