Y=-x2+5x+6

Solution for Y=-x2+5x+6 equation:

=-Y2+5Y+6

We move all terms to the left:

-(-Y2+5Y+6)=0

We add all the numbers together, and all the variables

-(-1Y^2+5Y+6)=0

We get rid of parentheses

1Y^2-5Y-6=0

We add all the numbers together, and all the variables

Y^2-5Y-6=0

a = 1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*1}=\frac{-2}{2}
=-1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*1}=\frac{12}{2}
=6
$