y+5=1/2y+6

Solution for y+5=1/2y+6 equation:

y+5=1/2y+6

We move all terms to the left:

y+5-(1/2y+6)=0


Domain of the equation: 2y+6)!=0

y∈R


We get rid of parentheses

y-1/2y-6+5=0

We multiply all the terms by the denominator


y*2y-6*2y+5*2y-1=0

Wy multiply elements

2y^2-12y+10y-1=0

We add all the numbers together, and all the variables

2y^2-2y-1=0

a = 2; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·2·(-1)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*2}=\frac{2-2\sqrt{3}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*2}=\frac{2+2\sqrt{3}}{4}
$