1/10x^2=20

Solution for 1/10x^2=20 equation:

1/10x^2=20

We move all terms to the left:

1/10x^2-(20)=0


Domain of the equation: 10x^2!=0

x^2!=0/10

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-20*10x^2+1=0

Wy multiply elements

-200x^2+1=0

a = -200; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-200)·1
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*-200}=\frac{0-20\sqrt{2}}{-400}
=-\frac{20\sqrt{2}}{-400}
=-\frac{\sqrt{2}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*-200}=\frac{0+20\sqrt{2}}{-400}
=\frac{20\sqrt{2}}{-400}
=\frac{\sqrt{2}}{-20}
$