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

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

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

We move all terms to the left:

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


Domain of the equation: 9b!=0

b!=0/9

b!=0

b∈R



Domain of the equation: 2b-7)!=0

b∈R


We get rid of parentheses

-2/9b-1/2b+7+3=0

We calculate fractions


(-4b)/18b^2+(-9b)/18b^2+7+3=0

We add all the numbers together, and all the variables

(-4b)/18b^2+(-9b)/18b^2+10=0

We multiply all the terms by the denominator


(-4b)+(-9b)+10*18b^2=0

Wy multiply elements

180b^2+(-4b)+(-9b)=0

We get rid of parentheses

180b^2-4b-9b=0

We add all the numbers together, and all the variables

180b^2-13b=0

a = 180; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·180·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*180}=\frac{0}{360}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*180}=\frac{26}{360}
=13/180
$