6(6)+11(11)=b^2

Solution for 6(6)+11(11)=b^2 equation:

6(6)+11(11)=b^2

We move all terms to the left:

6(6)+11(11)-(b^2)=0

We add all the numbers together, and all the variables

-1b^2+1177=0

a = -1; b = 0; c = +1177;
Δ = b2-4ac
Δ = 02-4·(-1)·1177
Δ = 4708
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:

$\sqrt{\Delta}=\sqrt{4708}=\sqrt{4*1177}=\sqrt{4}*\sqrt{1177}=2\sqrt{1177}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1177}}{2*-1}=\frac{0-2\sqrt{1177}}{-2}
=-\frac{2\sqrt{1177}}{-2}
=-\frac{\sqrt{1177}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1177}}{2*-1}=\frac{0+2\sqrt{1177}}{-2}
=\frac{2\sqrt{1177}}{-2}
=\frac{\sqrt{1177}}{-1}
$