3-2-9b=1/3b-7

Solution for 3-2-9b=1/3b-7 equation:

3-2-9b=1/3b-7

We move all terms to the left:

3-2-9b-(1/3b-7)=0


Domain of the equation: 3b-7)!=0

b∈R


We add all the numbers together, and all the variables

-9b-(1/3b-7)+1=0

We get rid of parentheses

-9b-1/3b+7+1=0

We multiply all the terms by the denominator


-9b*3b+7*3b+1*3b-1=0

Wy multiply elements

-27b^2+21b+3b-1=0

We add all the numbers together, and all the variables

-27b^2+24b-1=0

a = -27; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-27)·(-1)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{13}}{2*-27}=\frac{-24-6\sqrt{13}}{-54}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{13}}{2*-27}=\frac{-24+6\sqrt{13}}{-54}
$