Y=48x-4x^2

Solution for Y=48x-4x^2 equation:

=48Y-4Y^2

We move all terms to the left:

-(48Y-4Y^2)=0

We get rid of parentheses

4Y^2-48Y=0

a = 4; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·4·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*4}=\frac{0}{8}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*4}=\frac{96}{8}
=12
$