(16X)^2+(9x)^2=47^2

Solution for (16X)^2+(9x)^2=47^2 equation:

(16X)^2+(9X)^2=47^2

We move all terms to the left:

(16X)^2+(9X)^2-(47^2)=0

We add all the numbers together, and all the variables

25X^2-2209=0

a = 25; b = 0; c = -2209;
Δ = b2-4ac
Δ = 02-4·25·(-2209)
Δ = 220900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{220900}=470$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-470}{2*25}=\frac{-470}{50}
=-9+2/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+470}{2*25}=\frac{470}{50}
=9+2/5
$