(9x)^2+(16x)^2=22500

Solution for (9x)^2+(16x)^2=22500 equation:

(9x)^2+(16x)^2=22500

We move all terms to the left:

(9x)^2+(16x)^2-(22500)=0

We add all the numbers together, and all the variables

25x^2-22500=0

a = 25; b = 0; c = -22500;
Δ = b2-4ac
Δ = 02-4·25·(-22500)
Δ = 2250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2250000}=1500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1500}{2*25}=\frac{-1500}{50}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1500}{2*25}=\frac{1500}{50}
=30
$