-5/2w+4/3=-7/6w-1

Solution for -5/2w+4/3=-7/6w-1 equation:

-5/2w+4/3=-7/6w-1

We move all terms to the left:

-5/2w+4/3-(-7/6w-1)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 6w-1)!=0

w∈R


We get rid of parentheses

-5/2w+7/6w+1+4/3=0

We calculate fractions


288w^2/108w^2+(-270w)/108w^2+126w/108w^2+1=0

We multiply all the terms by the denominator


288w^2+(-270w)+126w+1*108w^2=0

We add all the numbers together, and all the variables

288w^2+126w+(-270w)+1*108w^2=0

Wy multiply elements

288w^2+108w^2+126w+(-270w)=0

We get rid of parentheses

288w^2+108w^2+126w-270w=0

We add all the numbers together, and all the variables

396w^2-144w=0

a = 396; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·396·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*396}=\frac{0}{792}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*396}=\frac{288}{792}
=4/11
$