(9x)^2+(16x)^2=55^2

Solution for (9x)^2+(16x)^2=55^2 equation:

(9x)^2+(16x)^2=55^2

We move all terms to the left:

(9x)^2+(16x)^2-(55^2)=0

We add all the numbers together, and all the variables

25x^2-3025=0

a = 25; b = 0; c = -3025;
Δ = b2-4ac
Δ = 02-4·25·(-3025)
Δ = 302500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{302500}=550$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-550}{2*25}=\frac{-550}{50}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+550}{2*25}=\frac{550}{50}
=11
$