3x^2=200^2

Solution for 3x^2=200^2 equation:

3x^2=200^2

We move all terms to the left:

3x^2-(200^2)=0

We add all the numbers together, and all the variables

3x^2-40000=0

a = 3; b = 0; c = -40000;
Δ = b2-4ac
Δ = 02-4·3·(-40000)
Δ = 480000
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:

$\sqrt{\Delta}=\sqrt{480000}=\sqrt{160000*3}=\sqrt{160000}*\sqrt{3}=400\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{3}}{2*3}=\frac{0-400\sqrt{3}}{6}
=-\frac{400\sqrt{3}}{6}
=-\frac{200\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{3}}{2*3}=\frac{0+400\sqrt{3}}{6}
=\frac{400\sqrt{3}}{6}
=\frac{200\sqrt{3}}{3}
$