Y=-x^2-5x+12

Solution for Y=-x^2-5x+12 equation:

=-Y^2-5Y+12

We move all terms to the left:

-(-Y^2-5Y+12)=0

We get rid of parentheses

Y^2+5Y-12=0

a = 1; b = 5; c = -12;
Δ = b2-4ac
Δ = 52-4·1·(-12)
Δ = 73
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{-(5)-\sqrt{73}}{2*1}=\frac{-5-\sqrt{73}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*1}=\frac{-5+\sqrt{73}}{2}
$