(11*11)+(b*b)=12*12

Solution for (11*11)+(b*b)=12*12 equation:

(11*11)+(b*b)=12*12

We move all terms to the left:

(11*11)+(b*b)-(12*12)=0

We add all the numbers together, and all the variables

(+b*b)+121-144=0

We add all the numbers together, and all the variables

(+b*b)-23=0

We get rid of parentheses

b*b-23=0

Wy multiply elements

b^2-23=0

a = 1; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·1·(-23)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{23}}{2*1}=\frac{0-2\sqrt{23}}{2}
=-\frac{2\sqrt{23}}{2}
=-\sqrt{23}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{23}}{2*1}=\frac{0+2\sqrt{23}}{2}
=\frac{2\sqrt{23}}{2}
=\sqrt{23}
$