4+4/5b=9/10b

Solution for 4+4/5b=9/10b equation:

4+4/5b=9/10b

We move all terms to the left:

4+4/5b-(9/10b)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 10b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

4/5b-(+9/10b)+4=0

We get rid of parentheses

4/5b-9/10b+4=0

We calculate fractions


40b/50b^2+(-45b)/50b^2+4=0

We multiply all the terms by the denominator


40b+(-45b)+4*50b^2=0

Wy multiply elements

200b^2+40b+(-45b)=0

We get rid of parentheses

200b^2+40b-45b=0

We add all the numbers together, and all the variables

200b^2-5b=0

a = 200; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·200·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*200}=\frac{0}{400}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*200}=\frac{10}{400}
=1/40
$