x=1/2x+11

Solution for x=1/2x+11 equation:

x=1/2x+11

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-1/2x-11=0

We multiply all the terms by the denominator


x*2x-11*2x-1=0

Wy multiply elements

2x^2-22x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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