H(x)=3x^2+2x

Solution for H(x)=3x^2+2x equation:

(H)=3H^2+2H

We move all terms to the left:

(H)-(3H^2+2H)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3H^2-1H=0

a = -3; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-3)·0
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{-(-1)-1}{2*-3}=\frac{0}{-6}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-3}=\frac{2}{-6}
=-1/3
$