y=6-1/2y

Solution for y=6-1/2y equation:

y=6-1/2y

We move all terms to the left:

y-(6-1/2y)=0


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(-1/2y+6)=0

We get rid of parentheses

y+1/2y-6=0

We multiply all the terms by the denominator


y*2y-6*2y+1=0

Wy multiply elements

2y^2-12y+1=0

a = 2; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·2·1
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{34}}{2*2}=\frac{12-2\sqrt{34}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{34}}{2*2}=\frac{12+2\sqrt{34}}{4}
$