F(x)=1/2x+8

Solution for F(x)=1/2x+8 equation:

(F)=1/2F+8

We move all terms to the left:

(F)-(1/2F+8)=0


Domain of the equation: 2F+8)!=0

F∈R


We get rid of parentheses

F-1/2F-8=0

We multiply all the terms by the denominator


F*2F-8*2F-1=0

Wy multiply elements

2F^2-16F-1=0

a = 2; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·2·(-1)
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{66}}{2*2}=\frac{16-2\sqrt{66}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{66}}{2*2}=\frac{16+2\sqrt{66}}{4}
$