1/4b-1/3b=1/2-2

Solution for 1/4b-1/3b=1/2-2 equation:

1/4b-1/3b=1/2-2

We move all terms to the left:

1/4b-1/3b-(1/2-2)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We get rid of parentheses

1/4b-1/3b+2-1/2=0

We calculate fractions


(-36b^2)/48b^2+12b/48b^2+(-16b)/48b^2+2=0

We multiply all the terms by the denominator


(-36b^2)+12b+(-16b)+2*48b^2=0

Wy multiply elements

(-36b^2)+96b^2+12b+(-16b)=0

We get rid of parentheses

-36b^2+96b^2+12b-16b=0

We add all the numbers together, and all the variables

60b^2-4b=0

a = 60; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·60·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*60}=\frac{0}{120}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*60}=\frac{8}{120}
=1/15
$