(16x)^2+(9x)^2=21.5^2

Solution for (16x)^2+(9x)^2=21.5^2 equation:

(16x)^2+(9x)^2=21.5^2

We move all terms to the left:

(16x)^2+(9x)^2-(21.5^2)=0

We add all the numbers together, and all the variables

25x^2-462.25=0

a = 25; b = 0; c = -462.25;
Δ = b2-4ac
Δ = 02-4·25·(-462.25)
Δ = 46225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46225}=215$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-215}{2*25}=\frac{-215}{50}
=-4+3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+215}{2*25}=\frac{215}{50}
=4+3/10
$