H(x)=x2-3x-4

Solution for H(x)=x2-3x-4 equation:

(H)=H2-3H-4

We move all terms to the left:

(H)-(H2-3H-4)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-1)·4
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-1}=\frac{-4-4\sqrt{2}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-1}=\frac{-4+4\sqrt{2}}{-2}
$