688b(6-67b)=12b

Solution for 688b(6-67b)=12b equation:

688b(6-67b)=12b

We move all terms to the left:

688b(6-67b)-(12b)=0

We add all the numbers together, and all the variables

688b(-67b+6)-12b=0

We add all the numbers together, and all the variables

-12b+688b(-67b+6)=0

We multiply parentheses

-46096b^2-12b+4128b=0

We add all the numbers together, and all the variables

-46096b^2+4116b=0

a = -46096; b = 4116; c = 0;
Δ = b2-4ac
Δ = 41162-4·(-46096)·0
Δ = 16941456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16941456}=4116$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4116)-4116}{2*-46096}=\frac{-8232}{-92192}
=1029/11524
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4116)+4116}{2*-46096}=\frac{0}{-92192}
=0
$