K(x)=1/2x+4

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

(K)=1/2K+4

We move all terms to the left:

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


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

K∈R


We get rid of parentheses

K-1/2K-4=0

We multiply all the terms by the denominator


K*2K-4*2K-1=0

Wy multiply elements

2K^2-8K-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:
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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