1/3w+w+2=7

Solution for 1/3w+w+2=7 equation:

1/3w+w+2=7

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

w+1/3w-5=0

We multiply all the terms by the denominator


w*3w-5*3w+1=0

Wy multiply elements

3w^2-15w+1=0

a = 3; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·3·1
Δ = 213
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{-(-15)-\sqrt{213}}{2*3}=\frac{15-\sqrt{213}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{213}}{2*3}=\frac{15+\sqrt{213}}{6}
$