16x^2+9x^2=108^2

Solution for 16x^2+9x^2=108^2 equation:

16x^2+9x^2=108^2

We move all terms to the left:

16x^2+9x^2-(108^2)=0

We add all the numbers together, and all the variables

25x^2-11664=0

a = 25; b = 0; c = -11664;
Δ = b2-4ac
Δ = 02-4·25·(-11664)
Δ = 1166400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1166400}=1080$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1080}{2*25}=\frac{-1080}{50}
=-21+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1080}{2*25}=\frac{1080}{50}
=21+3/5
$