(4x)^2+(3x)^2=30^2

Solution for (4x)^2+(3x)^2=30^2 equation:

(4x)^2+(3x)^2=30^2

We move all terms to the left:

(4x)^2+(3x)^2-(30^2)=0

We add all the numbers together, and all the variables

7x^2-900=0

a = 7; b = 0; c = -900;
Δ = b2-4ac
Δ = 02-4·7·(-900)
Δ = 25200
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:

$\sqrt{\Delta}=\sqrt{25200}=\sqrt{3600*7}=\sqrt{3600}*\sqrt{7}=60\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{7}}{2*7}=\frac{0-60\sqrt{7}}{14}
=-\frac{60\sqrt{7}}{14}
=-\frac{30\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{7}}{2*7}=\frac{0+60\sqrt{7}}{14}
=\frac{60\sqrt{7}}{14}
=\frac{30\sqrt{7}}{7}
$