H=-26t^2+75+4

Solution for H=-26t^2+75+4 equation:

=-26H^2+75+4

We move all terms to the left:

-(-26H^2+75+4)=0

We get rid of parentheses

26H^2-75-4=0

We add all the numbers together, and all the variables

26H^2-79=0

a = 26; b = 0; c = -79;
Δ = b2-4ac
Δ = 02-4·26·(-79)
Δ = 8216
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:

$\sqrt{\Delta}=\sqrt{8216}=\sqrt{4*2054}=\sqrt{4}*\sqrt{2054}=2\sqrt{2054}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2054}}{2*26}=\frac{0-2\sqrt{2054}}{52}
=-\frac{2\sqrt{2054}}{52}
=-\frac{\sqrt{2054}}{26}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2054}}{2*26}=\frac{0+2\sqrt{2054}}{52}
=\frac{2\sqrt{2054}}{52}
=\frac{\sqrt{2054}}{26}
$