3^2+x^2=33^2

Solution for 3^2+x^2=33^2 equation:

3^2+x^2=33^2

We move all terms to the left:

3^2+x^2-(33^2)=0

We add all the numbers together, and all the variables

x^2-1080=0

a = 1; b = 0; c = -1080;
Δ = b2-4ac
Δ = 02-4·1·(-1080)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{30}}{2*1}=\frac{0-12\sqrt{30}}{2}
=-\frac{12\sqrt{30}}{2}
=-6\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{30}}{2*1}=\frac{0+12\sqrt{30}}{2}
=\frac{12\sqrt{30}}{2}
=6\sqrt{30}
$