1/8b+b=8

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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} $

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