b=8b2-9

Solution for b=8b2-9 equation:

b=8b^2-9

We move all terms to the left:

b-(8b^2-9)=0

We get rid of parentheses

-8b^2+b+9=0

a = -8; b = 1; c = +9;
Δ = b2-4ac
Δ = 12-4·(-8)·9
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*-8}=\frac{-18}{-16}
=1+1/8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*-8}=\frac{16}{-16}
=-1
$