9/2b-5/b=5

Solution for 9/2b-5/b=5 equation:

9/2b-5/b=5

We move all terms to the left:

9/2b-5/b-(5)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: b!=0

b∈R


We calculate fractions


9b/2b^2+(-10b)/2b^2-5=0

We multiply all the terms by the denominator


9b+(-10b)-5*2b^2=0

Wy multiply elements

-10b^2+9b+(-10b)=0

We get rid of parentheses

-10b^2+9b-10b=0

We add all the numbers together, and all the variables

-10b^2-1b=0

a = -10; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-10)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-10}=\frac{0}{-20}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-10}=\frac{2}{-20}
=-1/10
$