b^2=747

Solution for b^2=747 equation:

b^2=747

We move all terms to the left:

b^2-(747)=0

a = 1; b = 0; c = -747;
Δ = b2-4ac
Δ = 02-4·1·(-747)
Δ = 2988
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:

$\sqrt{\Delta}=\sqrt{2988}=\sqrt{36*83}=\sqrt{36}*\sqrt{83}=6\sqrt{83}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{83}}{2*1}=\frac{0-6\sqrt{83}}{2}
=-\frac{6\sqrt{83}}{2}
=-3\sqrt{83}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{83}}{2*1}=\frac{0+6\sqrt{83}}{2}
=\frac{6\sqrt{83}}{2}
=3\sqrt{83}
$