H(x)=-4+1/2x

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

(H)=-4+1/2H

We move all terms to the left:

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


Domain of the equation: 2H)!=0

H!=0/1

H!=0

H∈R


We add all the numbers together, and all the variables

H-(1/2H-4)=0

We get rid of parentheses

H-1/2H+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

2H^2+8H-1=0

a = 2; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·2·(-1)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{2}}{2*2}=\frac{-8-6\sqrt{2}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{2}}{2*2}=\frac{-8+6\sqrt{2}}{4}
$