6+1/6b=3/10b

Solution for 6+1/6b=3/10b equation:

6+1/6b=3/10b

We move all terms to the left:

6+1/6b-(3/10b)=0


Domain of the equation: 6b!=0

b!=0/6

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

1/6b-(+3/10b)+6=0

We get rid of parentheses

1/6b-3/10b+6=0

We calculate fractions


10b/60b^2+(-18b)/60b^2+6=0

We multiply all the terms by the denominator


10b+(-18b)+6*60b^2=0

Wy multiply elements

360b^2+10b+(-18b)=0

We get rid of parentheses

360b^2+10b-18b=0

We add all the numbers together, and all the variables

360b^2-8b=0

a = 360; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·360·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*360}=\frac{0}{720}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*360}=\frac{16}{720}
=1/45
$