H(t)=-4t^2+6t-1

Solution for H(t)=-4t^2+6t-1 equation:

(H)=-4H^2+6H-1

We move all terms to the left:

(H)-(-4H^2+6H-1)=0

We get rid of parentheses

4H^2-6H+H+1=0

We add all the numbers together, and all the variables

4H^2-5H+1=0

a = 4; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·4·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*4}=\frac{2}{8}
=1/4
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*4}=\frac{8}{8}
=1
$