0.1x^2=100

Solution for 0.1x^2=100 equation:

0.1x^2=100

We move all terms to the left:

0.1x^2-(100)=0

a = 0.1; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·0.1·(-100)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*0.1}=\frac{0-2\sqrt{10}}{0.2}
=-\frac{2\sqrt{10}}{0.2}
=-\frac{\sqrt{10}}{0.1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*0.1}=\frac{0+2\sqrt{10}}{0.2}
=\frac{2\sqrt{10}}{0.2}
=\frac{\sqrt{10}}{0.1}
$