-7/6w+5/2=-2/3w-3

Solution for -7/6w+5/2=-2/3w-3 equation:

-7/6w+5/2=-2/3w-3

We move all terms to the left:

-7/6w+5/2-(-2/3w-3)=0


Domain of the equation: 6w!=0

w!=0/6

w!=0

w∈R



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

w∈R


We get rid of parentheses

-7/6w+2/3w+3+5/2=0

We calculate fractions


270w^2/72w^2+(-84w)/72w^2+48w/72w^2+3=0

We multiply all the terms by the denominator


270w^2+(-84w)+48w+3*72w^2=0

We add all the numbers together, and all the variables

270w^2+48w+(-84w)+3*72w^2=0

Wy multiply elements

270w^2+216w^2+48w+(-84w)=0

We get rid of parentheses

270w^2+216w^2+48w-84w=0

We add all the numbers together, and all the variables

486w^2-36w=0

a = 486; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·486·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*486}=\frac{0}{972}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*486}=\frac{72}{972}
=2/27
$