(3x)^2-x^2=22500

Solution for (3x)^2-x^2=22500 equation:

(3x)^2-x^2=22500

We move all terms to the left:

(3x)^2-x^2-(22500)=0

We add all the numbers together, and all the variables

2x^2-22500=0

a = 2; b = 0; c = -22500;
Δ = b2-4ac
Δ = 02-4·2·(-22500)
Δ = 180000
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:

$\sqrt{\Delta}=\sqrt{180000}=\sqrt{90000*2}=\sqrt{90000}*\sqrt{2}=300\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{2}}{2*2}=\frac{0-300\sqrt{2}}{4}
=-\frac{300\sqrt{2}}{4}
=-75\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{2}}{2*2}=\frac{0+300\sqrt{2}}{4}
=\frac{300\sqrt{2}}{4}
=75\sqrt{2}
$