Y=x^2-20x+96

Solution for Y=x^2-20x+96 equation:

=Y^2-20Y+96

We move all terms to the left:

-(Y^2-20Y+96)=0

We get rid of parentheses

-Y^2+20Y-96=0

We add all the numbers together, and all the variables

-1Y^2+20Y-96=0

a = -1; b = 20; c = -96;
Δ = b2-4ac
Δ = 202-4·(-1)·(-96)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4}{2*-1}=\frac{-24}{-2}
=+12
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4}{2*-1}=\frac{-16}{-2}
=+8
$