(4x)^2+(3x)^2=83

Solution for (4x)^2+(3x)^2=83 equation:

(4x)^2+(3x)^2=83

We move all terms to the left:

(4x)^2+(3x)^2-(83)=0

We add all the numbers together, and all the variables

7x^2-83=0

a = 7; b = 0; c = -83;
Δ = b2-4ac
Δ = 02-4·7·(-83)
Δ = 2324
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:

$\sqrt{\Delta}=\sqrt{2324}=\sqrt{4*581}=\sqrt{4}*\sqrt{581}=2\sqrt{581}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{581}}{2*7}=\frac{0-2\sqrt{581}}{14}
=-\frac{2\sqrt{581}}{14}
=-\frac{\sqrt{581}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{581}}{2*7}=\frac{0+2\sqrt{581}}{14}
=\frac{2\sqrt{581}}{14}
=\frac{\sqrt{581}}{7}
$