H(1.5)=t^2-2t

Solution for H(1.5)=t^2-2t equation:

(1.5)=H^2-2H

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(H^2-2H)+1.5=0

We get rid of parentheses

-H^2+2H+1.5=0

We add all the numbers together, and all the variables

-1H^2+2H+1.5=0

a = -1; b = 2; c = +1.5;
Δ = b2-4ac
Δ = 22-4·(-1)·1.5
Δ = 10
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-\sqrt{10}}{2*-1}=\frac{-2-\sqrt{10}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{10}}{2*-1}=\frac{-2+\sqrt{10}}{-2}
$