4x^2+36x^2=200^2

Solution for 4x^2+36x^2=200^2 equation:

4x^2+36x^2=200^2

We move all terms to the left:

4x^2+36x^2-(200^2)=0

We add all the numbers together, and all the variables

40x^2-40000=0

a = 40; b = 0; c = -40000;
Δ = b2-4ac
Δ = 02-4·40·(-40000)
Δ = 6400000
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:

$\sqrt{\Delta}=\sqrt{6400000}=\sqrt{640000*10}=\sqrt{640000}*\sqrt{10}=800\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{10}}{2*40}=\frac{0-800\sqrt{10}}{80}
=-\frac{800\sqrt{10}}{80}
=-10\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{10}}{2*40}=\frac{0+800\sqrt{10}}{80}
=\frac{800\sqrt{10}}{80}
=10\sqrt{10}
$