45^2+36^2=x^2

Solution for 45^2+36^2=x^2 equation:

45^2+36^2=x^2

We move all terms to the left:

45^2+36^2-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+3321=0

a = -1; b = 0; c = +3321;
Δ = b2-4ac
Δ = 02-4·(-1)·3321
Δ = 13284
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:

$\sqrt{\Delta}=\sqrt{13284}=\sqrt{324*41}=\sqrt{324}*\sqrt{41}=18\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{41}}{2*-1}=\frac{0-18\sqrt{41}}{-2}
=-\frac{18\sqrt{41}}{-2}
=-\frac{9\sqrt{41}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{41}}{2*-1}=\frac{0+18\sqrt{41}}{-2}
=\frac{18\sqrt{41}}{-2}
=\frac{9\sqrt{41}}{-1}
$