12b(10-7b)=7b+1

Solution for 12b(10-7b)=7b+1 equation:

12b(10-7b)=7b+1

We move all terms to the left:

12b(10-7b)-(7b+1)=0

We add all the numbers together, and all the variables

12b(-7b+10)-(7b+1)=0

We multiply parentheses

-84b^2+120b-(7b+1)=0

We get rid of parentheses

-84b^2+120b-7b-1=0

We add all the numbers together, and all the variables

-84b^2+113b-1=0

a = -84; b = 113; c = -1;
Δ = b2-4ac
Δ = 1132-4·(-84)·(-1)
Δ = 12433
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-\sqrt{12433}}{2*-84}=\frac{-113-\sqrt{12433}}{-168}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+\sqrt{12433}}{2*-84}=\frac{-113+\sqrt{12433}}{-168}
$