Y=-16x^2+27x+4

Solution for Y=-16x^2+27x+4 equation:

=-16Y^2+27Y+4

We move all terms to the left:

-(-16Y^2+27Y+4)=0

We get rid of parentheses

16Y^2-27Y-4=0

a = 16; b = -27; c = -4;
Δ = b2-4ac
Δ = -272-4·16·(-4)
Δ = 985
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{-(-27)-\sqrt{985}}{2*16}=\frac{27-\sqrt{985}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{985}}{2*16}=\frac{27+\sqrt{985}}{32}
$