2000=0.290W/t2

Solution for 2000=0.290W/t2 equation:

2000=0.290/W2

We move all terms to the left:

2000-(0.290/W2)=0


Domain of the equation: W2)!=0

W!=0/1

W!=0

W∈R


We add all the numbers together, and all the variables

-(+0.290/W2)+2000=0

We get rid of parentheses

-0.290/W2+2000=0

We multiply all the terms by the denominator


2000*W2-0.290=0

We add all the numbers together, and all the variables

2000W^2-0.29=0

a = 2000; b = 0; c = -0.29;
Δ = b2-4ac
Δ = 02-4·2000·(-0.29)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{145}}{2*2000}=\frac{0-4\sqrt{145}}{4000}
=-\frac{4\sqrt{145}}{4000}
=-\frac{\sqrt{145}}{1000}
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{145}}{2*2000}=\frac{0+4\sqrt{145}}{4000}
=\frac{4\sqrt{145}}{4000}
=\frac{\sqrt{145}}{1000}
$