1-8b2=-33

Solution for 1-8b2=-33 equation:

1-8b^2=-33

We move all terms to the left:

1-8b^2-(-33)=0

We add all the numbers together, and all the variables

-8b^2+34=0

a = -8; b = 0; c = +34;
Δ = b2-4ac
Δ = 02-4·(-8)·34
Δ = 1088
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:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{17}}{2*-8}=\frac{0-8\sqrt{17}}{-16}
=-\frac{8\sqrt{17}}{-16}
=-\frac{\sqrt{17}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{17}}{2*-8}=\frac{0+8\sqrt{17}}{-16}
=\frac{8\sqrt{17}}{-16}
=\frac{\sqrt{17}}{-2}
$