2/5b+1/10=3/2b

Solution for 2/5b+1/10=3/2b equation:

2/5b+1/10=3/2b

We move all terms to the left:

2/5b+1/10-(3/2b)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 2b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

2/5b-(+3/2b)+1/10=0

We get rid of parentheses

2/5b-3/2b+1/10=0

We calculate fractions


20b^2/100b^2+40b/100b^2+(-150b)/100b^2=0

We multiply all the terms by the denominator


20b^2+40b+(-150b)=0

We get rid of parentheses

20b^2+40b-150b=0

We add all the numbers together, and all the variables

20b^2-110b=0

a = 20; b = -110; c = 0;
Δ = b2-4ac
Δ = -1102-4·20·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-110}{2*20}=\frac{0}{40}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+110}{2*20}=\frac{220}{40}
=5+1/2
$