6*6+b*b=24*24

Solution for 6*6+b*b=24*24 equation:

6*6+b*b=24*24

We move all terms to the left:

6*6+b*b-(24*24)=0

We add all the numbers together, and all the variables

b*b+6*6-576=0

We add all the numbers together, and all the variables

b*b-540=0

Wy multiply elements

b^2-540=0

a = 1; b = 0; c = -540;
Δ = b2-4ac
Δ = 02-4·1·(-540)
Δ = 2160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*1}=\frac{0-12\sqrt{15}}{2}
=-\frac{12\sqrt{15}}{2}
=-6\sqrt{15}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*1}=\frac{0+12\sqrt{15}}{2}
=\frac{12\sqrt{15}}{2}
=6\sqrt{15}
$