36*36+d*d=96*96

Solution for 36*36+d*d=96*96 equation:

36*36+d*d=96*96

We move all terms to the left:

36*36+d*d-(96*96)=0

We add all the numbers together, and all the variables

d*d+36*36-9216=0

We add all the numbers together, and all the variables

d*d-7920=0

Wy multiply elements

d^2-7920=0

a = 1; b = 0; c = -7920;
Δ = b2-4ac
Δ = 02-4·1·(-7920)
Δ = 31680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{31680}=\sqrt{576*55}=\sqrt{576}*\sqrt{55}=24\sqrt{55}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{55}}{2*1}=\frac{0-24\sqrt{55}}{2}
=-\frac{24\sqrt{55}}{2}
=-12\sqrt{55}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{55}}{2*1}=\frac{0+24\sqrt{55}}{2}
=\frac{24\sqrt{55}}{2}
=12\sqrt{55}
$