H=-16x^2+38x+5

Solution for H=-16x^2+38x+5 equation:

=-16H^2+38H+5

We move all terms to the left:

-(-16H^2+38H+5)=0

We get rid of parentheses

16H^2-38H-5=0

a = 16; b = -38; c = -5;
Δ = b2-4ac
Δ = -382-4·16·(-5)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-42}{2*16}=\frac{-4}{32}
=-1/8
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+42}{2*16}=\frac{80}{32}
=2+1/2
$