1/2b-1/3b=5/42

Solution for 1/2b-1/3b=5/42 equation:

1/2b-1/3b=5/42

We move all terms to the left:

1/2b-1/3b-(5/42)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

1/2b-1/3b-(+5/42)=0

We get rid of parentheses

1/2b-1/3b-5/42=0

We calculate fractions


(-90b^2)/1008b^2+504b/1008b^2+(-336b)/1008b^2=0

We multiply all the terms by the denominator


(-90b^2)+504b+(-336b)=0

We get rid of parentheses

-90b^2+504b-336b=0

We add all the numbers together, and all the variables

-90b^2+168b=0

a = -90; b = 168; c = 0;
Δ = b2-4ac
Δ = 1682-4·(-90)·0
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-168}{2*-90}=\frac{-336}{-180}
=1+13/15
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+168}{2*-90}=\frac{0}{-180}
=0
$