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 get rid of parentheses

-2.9b-1/3b+7+3=0

We multiply all the terms by the denominator


-(2.9b)*3b+7*3b+3*3b-1=0

We add all the numbers together, and all the variables

-(+2.9b)*3b+7*3b+3*3b-1=0

We multiply parentheses

-6b^2+7*3b+3*3b-1=0

Wy multiply elements

-6b^2+21b+9b-1=0

We add all the numbers together, and all the variables

-6b^2+30b-1=0

a = -6; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·(-6)·(-1)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{219}}{2*-6}=\frac{-30-2\sqrt{219}}{-12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{219}}{2*-6}=\frac{-30+2\sqrt{219}}{-12}
$