b/8b-7=7b-2

Solution for b/8b-7=7b-2 equation:

b/8b-7=7b-2

We move all terms to the left:

b/8b-7-(7b-2)=0


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R


We get rid of parentheses

b/8b-7b+2-7=0

We multiply all the terms by the denominator


b-7b*8b+2*8b-7*8b=0

Wy multiply elements

-56b^2+b+16b-56b=0

We add all the numbers together, and all the variables

-56b^2-39b=0

a = -56; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·(-56)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*-56}=\frac{0}{-112}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*-56}=\frac{78}{-112}
=-39/56
$