-1/4b+6=8b+39

Solution for -1/4b+6=8b+39 equation:

-1/4b+6=8b+39

We move all terms to the left:

-1/4b+6-(8b+39)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We get rid of parentheses

-1/4b-8b-39+6=0

We multiply all the terms by the denominator


-8b*4b-39*4b+6*4b-1=0

Wy multiply elements

-32b^2-156b+24b-1=0

We add all the numbers together, and all the variables

-32b^2-132b-1=0

a = -32; b = -132; c = -1;
Δ = b2-4ac
Δ = -1322-4·(-32)·(-1)
Δ = 17296
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:

$\sqrt{\Delta}=\sqrt{17296}=\sqrt{16*1081}=\sqrt{16}*\sqrt{1081}=4\sqrt{1081}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-4\sqrt{1081}}{2*-32}=\frac{132-4\sqrt{1081}}{-64}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+4\sqrt{1081}}{2*-32}=\frac{132+4\sqrt{1081}}{-64}
$