b^2-3=507

Solution for b^2-3=507 equation:

b^2-3=507

We move all terms to the left:

b^2-3-(507)=0

We add all the numbers together, and all the variables

b^2-510=0

a = 1; b = 0; c = -510;
Δ = b2-4ac
Δ = 02-4·1·(-510)
Δ = 2040
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:

$\sqrt{\Delta}=\sqrt{2040}=\sqrt{4*510}=\sqrt{4}*\sqrt{510}=2\sqrt{510}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{510}}{2*1}=\frac{0-2\sqrt{510}}{2}
=-\frac{2\sqrt{510}}{2}
=-\sqrt{510}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{510}}{2*1}=\frac{0+2\sqrt{510}}{2}
=\frac{2\sqrt{510}}{2}
=\sqrt{510}
$