16x^2+9x^2=100^2

Solution for 16x^2+9x^2=100^2 equation:

16x^2+9x^2=100^2

We move all terms to the left:

16x^2+9x^2-(100^2)=0

We add all the numbers together, and all the variables

25x^2-10000=0

a = 25; b = 0; c = -10000;
Δ = b2-4ac
Δ = 02-4·25·(-10000)
Δ = 1000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1000000}=1000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1000}{2*25}=\frac{-1000}{50}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1000}{2*25}=\frac{1000}{50}
=20
$