2/3b-1/6b=75

Solution for 2/3b-1/6b=75 equation:

2/3b-1/6b=75

We move all terms to the left:

2/3b-1/6b-(75)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 6b!=0

b!=0/6

b!=0

b∈R


We calculate fractions


12b/18b^2+(-3b)/18b^2-75=0

We multiply all the terms by the denominator


12b+(-3b)-75*18b^2=0

Wy multiply elements

-1350b^2+12b+(-3b)=0

We get rid of parentheses

-1350b^2+12b-3b=0

We add all the numbers together, and all the variables

-1350b^2+9b=0

a = -1350; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-1350)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-1350}=\frac{-18}{-2700}
=1/150
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-1350}=\frac{0}{-2700}
=0
$