Y=-3x^2-12x-10

Solution for Y=-3x^2-12x-10 equation:

=-3Y^2-12Y-10

We move all terms to the left:

-(-3Y^2-12Y-10)=0

We get rid of parentheses

3Y^2+12Y+10=0

a = 3; b = 12; c = +10;
Δ = b2-4ac
Δ = 122-4·3·10
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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