H(x)=-1/2x-2

Solution for H(x)=-1/2x-2 equation:

(H)=-1/2H-2

We move all terms to the left:

(H)-(-1/2H-2)=0


Domain of the equation: 2H-2)!=0

H∈R


We get rid of parentheses

H+1/2H+2=0

We multiply all the terms by the denominator


H*2H+2*2H+1=0

Wy multiply elements

2H^2+4H+1=0

a = 2; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·2·1
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{2}}{2*2}=\frac{-4-2\sqrt{2}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{2}}{2*2}=\frac{-4+2\sqrt{2}}{4}
$