F(x)=1/2x+11

Solution for F(x)=1/2x+11 equation:

(F)=1/2F+11

We move all terms to the left:

(F)-(1/2F+11)=0


Domain of the equation: 2F+11)!=0

F∈R


We get rid of parentheses

F-1/2F-11=0

We multiply all the terms by the denominator


F*2F-11*2F-1=0

Wy multiply elements

2F^2-22F-1=0

a = 2; b = -22; c = -1;
Δ = b2-4ac
Δ = -222-4·2·(-1)
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{123}}{2*2}=\frac{22-2\sqrt{123}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{123}}{2*2}=\frac{22+2\sqrt{123}}{4}
$