Y=-16x2+9x+4

Solution for Y=-16x2+9x+4 equation:

=-16Y^2+9Y+4

We move all terms to the left:

-(-16Y^2+9Y+4)=0

We get rid of parentheses

16Y^2-9Y-4=0

a = 16; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·16·(-4)
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{337}}{2*16}=\frac{9-\sqrt{337}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{337}}{2*16}=\frac{9+\sqrt{337}}{32}
$