H(x)=1/2x+4

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

(H)=1/2H+4

We move all terms to the left:

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


Domain of the equation: 2H+4)!=0

H∈R


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}
$