100*x^2=200

Solution for 100*x^2=200 equation:

100x^2=200

We move all terms to the left:

100x^2-(200)=0

a = 100; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·100·(-200)
Δ = 80000
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:

$\sqrt{\Delta}=\sqrt{80000}=\sqrt{40000*2}=\sqrt{40000}*\sqrt{2}=200\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{2}}{2*100}=\frac{0-200\sqrt{2}}{200}
=-\frac{200\sqrt{2}}{200}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{2}}{2*100}=\frac{0+200\sqrt{2}}{200}
=\frac{200\sqrt{2}}{200}
=\sqrt{2}
$