Y=-3x^2-15x-17

Solution for Y=-3x^2-15x-17 equation:

=-3Y^2-15Y-17

We move all terms to the left:

-(-3Y^2-15Y-17)=0

We get rid of parentheses

3Y^2+15Y+17=0

a = 3; b = 15; c = +17;
Δ = b2-4ac
Δ = 152-4·3·17
Δ = 21
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{-(15)-\sqrt{21}}{2*3}=\frac{-15-\sqrt{21}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{21}}{2*3}=\frac{-15+\sqrt{21}}{6}
$