(30)2+(12)2=(x)2

Solution for (30)2+(12)2=(x)2 equation:

(30)2+(12)2=(x)2

We move all terms to the left:

(30)2+(12)2-((x)2)=0

determiningTheFunctionDomain
-x2+302+122=0

We add all the numbers together, and all the variables

-1x^2+424=0

a = -1; b = 0; c = +424;
Δ = b2-4ac
Δ = 02-4·(-1)·424
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{106}}{2*-1}=\frac{0-4\sqrt{106}}{-2}
=-\frac{4\sqrt{106}}{-2}
=-\frac{2\sqrt{106}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{106}}{2*-1}=\frac{0+4\sqrt{106}}{-2}
=\frac{4\sqrt{106}}{-2}
=\frac{2\sqrt{106}}{-1}
$