w^2+w=1/3

Solution for w^2+w=1/3 equation:

w^2+w=1/3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

w^2+w-1/3=0

We multiply all the terms by the denominator


w^2*3+w*3-1=0

Wy multiply elements

3w^2+3w-1=0

a = 3; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·3·(-1)
Δ = 21
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{-(3)-\sqrt{21}}{2*3}=\frac{-3-\sqrt{21}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{21}}{2*3}=\frac{-3+\sqrt{21}}{6}
$