w-2/3w=3

Solution for w-2/3w=3 equation:

w-2/3w=3

We move all terms to the left:

w-2/3w-(3)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We multiply all the terms by the denominator


w*3w-3*3w-2=0

Wy multiply elements

3w^2-9w-2=0

a = 3; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·3·(-2)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{105}}{2*3}=\frac{9-\sqrt{105}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*3}=\frac{9+\sqrt{105}}{6}
$