W(w+61/3w)=30

Solution for W(w+61/3w)=30 equation:

(W+61/3W)=30

We move all terms to the left:

(W+61/3W)-(30)=0


Domain of the equation: 3W)!=0

W!=0/1

W!=0

W∈R


We add all the numbers together, and all the variables

(+W+61/3W)-30=0

We get rid of parentheses

W+61/3W-30=0

We multiply all the terms by the denominator


W*3W-30*3W+61=0

Wy multiply elements

3W^2-90W+61=0

a = 3; b = -90; c = +61;
Δ = b2-4ac
Δ = -902-4·3·61
Δ = 7368
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:

$\sqrt{\Delta}=\sqrt{7368}=\sqrt{4*1842}=\sqrt{4}*\sqrt{1842}=2\sqrt{1842}$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1842}}{2*3}=\frac{90-2\sqrt{1842}}{6}
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1842}}{2*3}=\frac{90+2\sqrt{1842}}{6}
$