(1/5)w=32

Solution for (1/5)w=32 equation:

(1/5)w=32

We move all terms to the left:

(1/5)w-(32)=0


Domain of the equation: 5)w!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

(+1/5)w-32=0

We multiply parentheses

w^2-32=0

a = 1; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·1·(-32)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2}}{2*1}=\frac{0-8\sqrt{2}}{2}
=-\frac{8\sqrt{2}}{2}
=-4\sqrt{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2}}{2*1}=\frac{0+8\sqrt{2}}{2}
=\frac{8\sqrt{2}}{2}
=4\sqrt{2}
$