(16x)^2+(9x)^2=30830

Solution for (16x)^2+(9x)^2=30830 equation:

(16x)^2+(9x)^2=30830

We move all terms to the left:

(16x)^2+(9x)^2-(30830)=0

We add all the numbers together, and all the variables

25x^2-30830=0

a = 25; b = 0; c = -30830;
Δ = b2-4ac
Δ = 02-4·25·(-30830)
Δ = 3083000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3083000}=\sqrt{100*30830}=\sqrt{100}*\sqrt{30830}=10\sqrt{30830}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{30830}}{2*25}=\frac{0-10\sqrt{30830}}{50}
=-\frac{10\sqrt{30830}}{50}
=-\frac{\sqrt{30830}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{30830}}{2*25}=\frac{0+10\sqrt{30830}}{50}
=\frac{10\sqrt{30830}}{50}
=\frac{\sqrt{30830}}{5}
$