Y=-x2+14x-24

Solution for Y=-x2+14x-24 equation:

=-Y2+14Y-24

We move all terms to the left:

-(-Y2+14Y-24)=0

We add all the numbers together, and all the variables

-(-1Y^2+14Y-24)=0

We get rid of parentheses

1Y^2-14Y+24=0

We add all the numbers together, and all the variables

Y^2-14Y+24=0

a = 1; b = -14; c = +24;
Δ = b2-4ac
Δ = -142-4·1·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*1}=\frac{4}{2}
=2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*1}=\frac{24}{2}
=12
$