1/8b+b=8

Solution for 1/8b+b=8 equation:

1/8b+b=8

We move all terms to the left:

1/8b+b-(8)=0


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R


We add all the numbers together, and all the variables

b+1/8b-8=0

We multiply all the terms by the denominator


b*8b-8*8b+1=0

Wy multiply elements

8b^2-64b+1=0

a = 8; b = -64; c = +1;
Δ = b2-4ac
Δ = -642-4·8·1
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{-(-64)-4\sqrt{254}}{2*8}=\frac{64-4\sqrt{254}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{254}}{2*8}=\frac{64+4\sqrt{254}}{16}
$