8b(3b+4)=1

Solution for 8b(3b+4)=1 equation:

8b(3b+4)=1

We move all terms to the left:

8b(3b+4)-(1)=0

We multiply parentheses

24b^2+32b-1=0

a = 24; b = 32; c = -1;
Δ = b2-4ac
Δ = 322-4·24·(-1)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{70}}{2*24}=\frac{-32-4\sqrt{70}}{48}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{70}}{2*24}=\frac{-32+4\sqrt{70}}{48}
$