-1/3w+2/3=-7/2w-6

Solution for -1/3w+2/3=-7/2w-6 equation:

-1/3w+2/3=-7/2w-6

We move all terms to the left:

-1/3w+2/3-(-7/2w-6)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 2w-6)!=0

w∈R


We get rid of parentheses

-1/3w+7/2w+6+2/3=0

We calculate fractions


(-2w)/54w^2+189w/54w^2+4w/54w^2+6=0

We multiply all the terms by the denominator


(-2w)+189w+4w+6*54w^2=0

We add all the numbers together, and all the variables

193w+(-2w)+6*54w^2=0

Wy multiply elements

324w^2+193w+(-2w)=0

We get rid of parentheses

324w^2+193w-2w=0

We add all the numbers together, and all the variables

324w^2+191w=0

a = 324; b = 191; c = 0;
Δ = b2-4ac
Δ = 1912-4·324·0
Δ = 36481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36481}=191$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(191)-191}{2*324}=\frac{-382}{648}
=-191/324
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(191)+191}{2*324}=\frac{0}{648}
=0
$