4b^2-2=182

Solution for 4b^2-2=182 equation:

4b^2-2=182

We move all terms to the left:

4b^2-2-(182)=0

We add all the numbers together, and all the variables

4b^2-184=0

a = 4; b = 0; c = -184;
Δ = b2-4ac
Δ = 02-4·4·(-184)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{46}}{2*4}=\frac{0-8\sqrt{46}}{8}
=-\frac{8\sqrt{46}}{8}
=-\sqrt{46}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{46}}{2*4}=\frac{0+8\sqrt{46}}{8}
=\frac{8\sqrt{46}}{8}
=\sqrt{46}
$