2w+16=2/5w

Solution for 2w+16=2/5w equation:

2w+16=2/5w

We move all terms to the left:

2w+16-(2/5w)=0


Domain of the equation: 5w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

2w-(+2/5w)+16=0

We get rid of parentheses

2w-2/5w+16=0

We multiply all the terms by the denominator


2w*5w+16*5w-2=0

Wy multiply elements

10w^2+80w-2=0

a = 10; b = 80; c = -2;
Δ = b2-4ac
Δ = 802-4·10·(-2)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-36\sqrt{5}}{2*10}=\frac{-80-36\sqrt{5}}{20}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+36\sqrt{5}}{2*10}=\frac{-80+36\sqrt{5}}{20}
$