Y=-16x^2+9x+3.25

Solution for Y=-16x^2+9x+3.25 equation:

=-16Y^2+9Y+3.25

We move all terms to the left:

-(-16Y^2+9Y+3.25)=0

We get rid of parentheses

16Y^2-9Y-3.25=0

a = 16; b = -9; c = -3.25;
Δ = b2-4ac
Δ = -92-4·16·(-3.25)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-17}{2*16}=\frac{-8}{32}
=-1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+17}{2*16}=\frac{26}{32}
=13/16
$