100*6^2=400*x^2

Solution for 100*6^2=400*x^2 equation:

100*6^2=400x^2

We move all terms to the left:

100*6^2-(400x^2)=0

We add all the numbers together, and all the variables

-400x^2+3600=0

a = -400; b = 0; c = +3600;
Δ = b2-4ac
Δ = 02-4·(-400)·3600
Δ = 5760000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5760000}=2400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2400}{2*-400}=\frac{-2400}{-800}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2400}{2*-400}=\frac{2400}{-800}
=-3
$