H(t)=t^2t-t^2/2

Solution for H(t)=t^2t-t^2/2 equation:

(H)=H^2H-H^2/2

We move all terms to the left:

(H)-(H^2H-H^2/2)=0

We get rid of parentheses

-H^2H+H^2/2+H=0

We multiply all the terms by the denominator


H^2-H^2H*2+H*2=0

Wy multiply elements

H^2-2H^2+2H=0

We add all the numbers together, and all the variables

-1H^2+2H=0

a = -1; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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