w+6=1/2w+10

Solution for w+6=1/2w+10 equation:

w+6=1/2w+10

We move all terms to the left:

w+6-(1/2w+10)=0


Domain of the equation: 2w+10)!=0

w∈R


We get rid of parentheses

w-1/2w-10+6=0

We multiply all the terms by the denominator


w*2w-10*2w+6*2w-1=0

Wy multiply elements

2w^2-20w+12w-1=0

We add all the numbers together, and all the variables

2w^2-8w-1=0

a = 2; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·2·(-1)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{2}}{2*2}=\frac{8-6\sqrt{2}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*2}=\frac{8+6\sqrt{2}}{4}
$