Y=35t-12t^2

Solution for Y=35t-12t^2 equation:

=35Y-12Y^2

We move all terms to the left:

-(35Y-12Y^2)=0

We get rid of parentheses

12Y^2-35Y=0

a = 12; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·12·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*12}=\frac{0}{24}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*12}=\frac{70}{24}
=2+11/12
$