H(x)=3x^2-12x+5

Solution for H(x)=3x^2-12x+5 equation:

(H)=3H^2-12H+5

We move all terms to the left:

(H)-(3H^2-12H+5)=0

We get rid of parentheses

-3H^2+H+12H-5=0

We add all the numbers together, and all the variables

-3H^2+13H-5=0

a = -3; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·(-3)·(-5)
Δ = 109
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{-(13)-\sqrt{109}}{2*-3}=\frac{-13-\sqrt{109}}{-6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{109}}{2*-3}=\frac{-13+\sqrt{109}}{-6}
$