H(x)=2x2+4x+1

Solution for H(x)=2x2+4x+1 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2H^2-3H-1=0

a = -2; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·(-2)·(-1)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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