4b^2+9=263

Solution for 4b^2+9=263 equation:

4b^2+9=263

We move all terms to the left:

4b^2+9-(263)=0

We add all the numbers together, and all the variables

4b^2-254=0

a = 4; b = 0; c = -254;
Δ = b2-4ac
Δ = 02-4·4·(-254)
Δ = 4064
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:

$\sqrt{\Delta}=\sqrt{4064}=\sqrt{16*254}=\sqrt{16}*\sqrt{254}=4\sqrt{254}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{254}}{2*4}=\frac{0-4\sqrt{254}}{8}
=-\frac{4\sqrt{254}}{8}
=-\frac{\sqrt{254}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{254}}{2*4}=\frac{0+4\sqrt{254}}{8}
=\frac{4\sqrt{254}}{8}
=\frac{\sqrt{254}}{2}
$