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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



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

w∈R


We get rid of parentheses

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

We calculate fractions


12w/18w^2+(-15w)/18w^2+1+3=0

We add all the numbers together, and all the variables

12w/18w^2+(-15w)/18w^2+4=0

We multiply all the terms by the denominator


12w+(-15w)+4*18w^2=0

Wy multiply elements

72w^2+12w+(-15w)=0

We get rid of parentheses

72w^2+12w-15w=0

We add all the numbers together, and all the variables

72w^2-3w=0

a = 72; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·72·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*72}=\frac{0}{144}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*72}=\frac{6}{144}
=1/24
$