3/2w+8=1/3w-7

Solution for 3/2w+8=1/3w-7 equation:

3/2w+8=1/3w-7

We move all terms to the left:

3/2w+8-(1/3w-7)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w-7)!=0

w∈R


We get rid of parentheses

3/2w-1/3w+7+8=0

We calculate fractions


9w/6w^2+(-2w)/6w^2+7+8=0

We add all the numbers together, and all the variables

9w/6w^2+(-2w)/6w^2+15=0

We multiply all the terms by the denominator


9w+(-2w)+15*6w^2=0

Wy multiply elements

90w^2+9w+(-2w)=0

We get rid of parentheses

90w^2+9w-2w=0

We add all the numbers together, and all the variables

90w^2+7w=0

a = 90; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·90·0
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*90}=\frac{-14}{180}
=-7/90
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*90}=\frac{0}{180}
=0
$