(4/5)*w=40

Solution for (4/5)*w=40 equation:

(4/5)*w=40

We move all terms to the left:

(4/5)*w-(40)=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

(+4/5)*w-40=0

We multiply parentheses

4w^2-40=0

a = 4; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·4·(-40)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*4}=\frac{0-8\sqrt{10}}{8}
=-\frac{8\sqrt{10}}{8}
=-\sqrt{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*4}=\frac{0+8\sqrt{10}}{8}
=\frac{8\sqrt{10}}{8}
=\sqrt{10}
$