3/5b-1/2b=1

Solution for 3/5b-1/2b=1 equation:

3/5b-1/2b=1

We move all terms to the left:

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


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We calculate fractions


6b/10b^2+(-5b)/10b^2-1=0

We multiply all the terms by the denominator


6b+(-5b)-1*10b^2=0

Wy multiply elements

-10b^2+6b+(-5b)=0

We get rid of parentheses

-10b^2+6b-5b=0

We add all the numbers together, and all the variables

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