w*10^-2=28.2

Solution for w*10^-2=28.2 equation:

w*10^-2=28.2

We move all terms to the left:

w*10^-2-(28.2)=0

We add all the numbers together, and all the variables

w*10^-30.2=0

Wy multiply elements

10w^2-30.2=0

a = 10; b = 0; c = -30.2;
Δ = b2-4ac
Δ = 02-4·10·(-30.2)
Δ = 1208
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:

$\sqrt{\Delta}=\sqrt{1208}=\sqrt{4*302}=\sqrt{4}*\sqrt{302}=2\sqrt{302}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{302}}{2*10}=\frac{0-2\sqrt{302}}{20}
=-\frac{2\sqrt{302}}{20}
=-\frac{\sqrt{302}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{302}}{2*10}=\frac{0+2\sqrt{302}}{20}
=\frac{2\sqrt{302}}{20}
=\frac{\sqrt{302}}{10}
$