Y=-12x2-33x+9

Solution for Y=-12x2-33x+9 equation:

=-12Y^2-33Y+9

We move all terms to the left:

-(-12Y^2-33Y+9)=0

We get rid of parentheses

12Y^2+33Y-9=0

a = 12; b = 33; c = -9;
Δ = b2-4ac
Δ = 332-4·12·(-9)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-39}{2*12}=\frac{-72}{24}
=-3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+39}{2*12}=\frac{6}{24}
=1/4
$