2/3w+8=-10-1/2w

Solution for 2/3w+8=-10-1/2w equation:

2/3w+8=-10-1/2w

We move all terms to the left:

2/3w+8-(-10-1/2w)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 2w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

2/3w-(-1/2w-10)+8=0

We get rid of parentheses

2/3w+1/2w+10+8=0

We calculate fractions


4w/6w^2+3w/6w^2+10+8=0

We add all the numbers together, and all the variables

4w/6w^2+3w/6w^2+18=0

We multiply all the terms by the denominator


4w+3w+18*6w^2=0

We add all the numbers together, and all the variables

7w+18*6w^2=0

Wy multiply elements

108w^2+7w=0

a = 108; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·108·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*108}=\frac{-14}{216}
=-7/108
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*108}=\frac{0}{216}
=0
$