3w=2+1/5w

Solution for 3w=2+1/5w equation:

3w=2+1/5w

We move all terms to the left:

3w-(2+1/5w)=0


Domain of the equation: 5w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

3w-(1/5w+2)=0

We get rid of parentheses

3w-1/5w-2=0

We multiply all the terms by the denominator


3w*5w-2*5w-1=0

Wy multiply elements

15w^2-10w-1=0

a = 15; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·15·(-1)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{10}}{2*15}=\frac{10-4\sqrt{10}}{30}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{10}}{2*15}=\frac{10+4\sqrt{10}}{30}
$