7/5b=2/b-3

Solution for 7/5b=2/b-3 equation:

7/5b=2/b-3

We move all terms to the left:

7/5b-(2/b-3)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



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

b∈R


We get rid of parentheses

7/5b-2/b+3=0

We calculate fractions


7b/5b^2+(-10b)/5b^2+3=0

We multiply all the terms by the denominator


7b+(-10b)+3*5b^2=0

Wy multiply elements

15b^2+7b+(-10b)=0

We get rid of parentheses

15b^2+7b-10b=0

We add all the numbers together, and all the variables

15b^2-3b=0

a = 15; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·15·0
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*15}=\frac{0}{30}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*15}=\frac{6}{30}
=1/5
$