x^2=(66^2)+(73^2)

Solution for x^2=(66^2)+(73^2) equation:

x^2=(66^2)+(73^2)

We move all terms to the left:

x^2-((66^2)+(73^2))=0

We add all the numbers together, and all the variables

x^2-9685=0

a = 1; b = 0; c = -9685;
Δ = b2-4ac
Δ = 02-4·1·(-9685)
Δ = 38740
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:

$\sqrt{\Delta}=\sqrt{38740}=\sqrt{4*9685}=\sqrt{4}*\sqrt{9685}=2\sqrt{9685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{9685}}{2*1}=\frac{0-2\sqrt{9685}}{2}
=-\frac{2\sqrt{9685}}{2}
=-\sqrt{9685}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{9685}}{2*1}=\frac{0+2\sqrt{9685}}{2}
=\frac{2\sqrt{9685}}{2}
=\sqrt{9685}
$