b-8/8b=12

Solution for b-8/8b=12 equation:

b-8/8b=12

We move all terms to the left:

b-8/8b-(12)=0


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R


We multiply all the terms by the denominator


b*8b-12*8b-8=0

Wy multiply elements

8b^2-96b-8=0

a = 8; b = -96; c = -8;
Δ = b2-4ac
Δ = -962-4·8·(-8)
Δ = 9472
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:

$\sqrt{\Delta}=\sqrt{9472}=\sqrt{256*37}=\sqrt{256}*\sqrt{37}=16\sqrt{37}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{37}}{2*8}=\frac{96-16\sqrt{37}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{37}}{2*8}=\frac{96+16\sqrt{37}}{16}
$