/w-2+2w=6+5w

Solution for /w-2+2w=6+5w equation:

/w-2+2w=6+5w

We move all terms to the left:

/w-2+2w-(6+5w)=0


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

/w+2w-(5w+6)-2=0

We add all the numbers together, and all the variables

2w+/w-(5w+6)-2=0

We get rid of parentheses

2w+/w-5w-6-2=0

We multiply all the terms by the denominator


2w*w-5w*w-6*w-2*w+=0

We add all the numbers together, and all the variables

-8w+2w*w-5w*w=0

Wy multiply elements

2w^2-5w^2-8w=0

We add all the numbers together, and all the variables

-3w^2-8w=0

a = -3; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-3)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-3}=\frac{0}{-6}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-3}=\frac{16}{-6}
=-2+2/3
$