Y=-3x^2-9x+1

Solution for Y=-3x^2-9x+1 equation:

=-3Y^2-9Y+1

We move all terms to the left:

-(-3Y^2-9Y+1)=0

We get rid of parentheses

3Y^2+9Y-1=0

a = 3; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·3·(-1)
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{93}}{2*3}=\frac{-9-\sqrt{93}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{93}}{2*3}=\frac{-9+\sqrt{93}}{6}
$