3=1/100x2

Solution for 3=1/100x2 equation:

3=1/100x^2

We move all terms to the left:

3-(1/100x^2)=0


Domain of the equation: 100x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/100x^2+3=0

We multiply all the terms by the denominator


3*100x^2-1=0

Wy multiply elements

300x^2-1=0

a = 300; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·300·(-1)
Δ = 1200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*300}=\frac{0-20\sqrt{3}}{600}
=-\frac{20\sqrt{3}}{600}
=-\frac{\sqrt{3}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*300}=\frac{0+20\sqrt{3}}{600}
=\frac{20\sqrt{3}}{600}
=\frac{\sqrt{3}}{30}
$