9/2b+7=3/b

Solution for 9/2b+7=3/b equation:

9/2b+7=3/b

We move all terms to the left:

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


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

9/2b-3/b+7=0

We calculate fractions


9b/2b^2+(-6b)/2b^2+7=0

We multiply all the terms by the denominator


9b+(-6b)+7*2b^2=0

Wy multiply elements

14b^2+9b+(-6b)=0

We get rid of parentheses

14b^2+9b-6b=0

We add all the numbers together, and all the variables

14b^2+3b=0

a = 14; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·14·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*14}=\frac{-6}{28}
=-3/14
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*14}=\frac{0}{28}
=0
$