b^2=1407

Solution for b^2=1407 equation:

b^2=1407

We move all terms to the left:

b^2-(1407)=0

a = 1; b = 0; c = -1407;
Δ = b2-4ac
Δ = 02-4·1·(-1407)
Δ = 5628
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:

$\sqrt{\Delta}=\sqrt{5628}=\sqrt{4*1407}=\sqrt{4}*\sqrt{1407}=2\sqrt{1407}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1407}}{2*1}=\frac{0-2\sqrt{1407}}{2}
=-\frac{2\sqrt{1407}}{2}
=-\sqrt{1407}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1407}}{2*1}=\frac{0+2\sqrt{1407}}{2}
=\frac{2\sqrt{1407}}{2}
=\sqrt{1407}
$