H(x)=2x^2-2x-4

Solution for H(x)=2x^2-2x-4 equation:

(H)=2H^2-2H-4

We move all terms to the left:

(H)-(2H^2-2H-4)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2H^2+3H+4=0

a = -2; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-2)·4
Δ = 41
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{-(3)-\sqrt{41}}{2*-2}=\frac{-3-\sqrt{41}}{-4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*-2}=\frac{-3+\sqrt{41}}{-4}
$