Y=-16x2+10x+4

Solution for Y=-16x2+10x+4 equation:

=-16Y^2+10Y+4

We move all terms to the left:

-(-16Y^2+10Y+4)=0

We get rid of parentheses

16Y^2-10Y-4=0

a = 16; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·16·(-4)
Δ = 356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{89}}{2*16}=\frac{10-2\sqrt{89}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{89}}{2*16}=\frac{10+2\sqrt{89}}{32}
$