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

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

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

We move all terms to the left:

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


Domain of the equation: b!=0

b∈R



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

b∈R


We get rid of parentheses

-2/b-1/3b+7+3=0

We calculate fractions


(-6b)/3b^2+(-b)/3b^2+7+3=0

We add all the numbers together, and all the variables

(-6b)/3b^2+(-1b)/3b^2+7+3=0

We add all the numbers together, and all the variables

(-6b)/3b^2+(-1b)/3b^2+10=0

We multiply all the terms by the denominator


(-6b)+(-1b)+10*3b^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

30b^2-7b=0

a = 30; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·30·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*30}=\frac{0}{60}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*30}=\frac{14}{60}
=7/30
$