H=-16t^2+26t-5

Solution for H=-16t^2+26t-5 equation:

=-16H^2+26H-5

We move all terms to the left:

-(-16H^2+26H-5)=0

We get rid of parentheses

16H^2-26H+5=0

a = 16; b = -26; c = +5;
Δ = b2-4ac
Δ = -262-4·16·5
Δ = 356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{89}}{2*16}=\frac{26-2\sqrt{89}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{89}}{2*16}=\frac{26+2\sqrt{89}}{32}
$