Y=-3x^2-12x+14

Solution for Y=-3x^2-12x+14 equation:

=-3Y^2-12Y+14

We move all terms to the left:

-(-3Y^2-12Y+14)=0

We get rid of parentheses

3Y^2+12Y-14=0

a = 3; b = 12; c = -14;
Δ = b2-4ac
Δ = 122-4·3·(-14)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{78}}{2*3}=\frac{-12-2\sqrt{78}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{78}}{2*3}=\frac{-12+2\sqrt{78}}{6}
$