x^2+49x^2=400^2

Solution for x^2+49x^2=400^2 equation:

x^2+49x^2=400^2

We move all terms to the left:

x^2+49x^2-(400^2)=0

We add all the numbers together, and all the variables

50x^2-160000=0

a = 50; b = 0; c = -160000;
Δ = b2-4ac
Δ = 02-4·50·(-160000)
Δ = 32000000
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:

$\sqrt{\Delta}=\sqrt{32000000}=\sqrt{16000000*2}=\sqrt{16000000}*\sqrt{2}=4000\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4000\sqrt{2}}{2*50}=\frac{0-4000\sqrt{2}}{100}
=-\frac{4000\sqrt{2}}{100}
=-40\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4000\sqrt{2}}{2*50}=\frac{0+4000\sqrt{2}}{100}
=\frac{4000\sqrt{2}}{100}
=40\sqrt{2}
$