7=5b-3/b

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

7=5b-3/b

We move all terms to the left:

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


Domain of the equation: b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-5b+3/b+7=0

We multiply all the terms by the denominator


-5b*b+7*b+3=0

We add all the numbers together, and all the variables

7b-5b*b+3=0

Wy multiply elements

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

a = -5; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·(-5)·3
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{109}}{2*-5}=\frac{-7-\sqrt{109}}{-10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{109}}{2*-5}=\frac{-7+\sqrt{109}}{-10}
$