A^2=276-b^2

Solution for A^2=276-b^2 equation:

^2=276-A^2

We move all terms to the left:

^2-(276-A^2)=0

We add all the numbers together, and all the variables

-(276-A^2)=0

We get rid of parentheses

A^2-276=0

a = 1; b = 0; c = -276;
Δ = b2-4ac
Δ = 02-4·1·(-276)
Δ = 1104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{69}}{2*1}=\frac{0-4\sqrt{69}}{2}
=-\frac{4\sqrt{69}}{2}
=-2\sqrt{69}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{69}}{2*1}=\frac{0+4\sqrt{69}}{2}
=\frac{4\sqrt{69}}{2}
=2\sqrt{69}
$