1/3w+w=20

Solution for 1/3w+w=20 equation:

1/3w+w=20

We move all terms to the left:

1/3w+w-(20)=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-20=0

We multiply all the terms by the denominator


w*3w-20*3w+1=0

Wy multiply elements

3w^2-60w+1=0

a = 3; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·3·1
Δ = 3588
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3588}=\sqrt{4*897}=\sqrt{4}*\sqrt{897}=2\sqrt{897}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{897}}{2*3}=\frac{60-2\sqrt{897}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{897}}{2*3}=\frac{60+2\sqrt{897}}{6}
$