9x^2+16x^2=400^2

Solution for 9x^2+16x^2=400^2 equation:

9x^2+16x^2=400^2

We move all terms to the left:

9x^2+16x^2-(400^2)=0

We add all the numbers together, and all the variables

25x^2-160000=0

a = 25; b = 0; c = -160000;
Δ = b2-4ac
Δ = 02-4·25·(-160000)
Δ = 16000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16000000}=4000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4000}{2*25}=\frac{-4000}{50}
=-80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4000}{2*25}=\frac{4000}{50}
=80
$