H=16t^2+76t+23

Solution for H=16t^2+76t+23 equation:

=16H^2+76H+23

We move all terms to the left:

-(16H^2+76H+23)=0

We get rid of parentheses

-16H^2-76H-23=0

a = -16; b = -76; c = -23;
Δ = b2-4ac
Δ = -762-4·(-16)·(-23)
Δ = 4304
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:

$\sqrt{\Delta}=\sqrt{4304}=\sqrt{16*269}=\sqrt{16}*\sqrt{269}=4\sqrt{269}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{269}}{2*-16}=\frac{76-4\sqrt{269}}{-32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{269}}{2*-16}=\frac{76+4\sqrt{269}}{-32}
$