(14)/(3)-1(1/2)b=b-(1)/(3)

Solution for (14)/(3)-1(1/2)b=b-(1)/(3) equation:

(14)/(3)-1(1/2)b=b-(1)/(3)

We move all terms to the left:

(14)/(3)-1(1/2)b-(b-(1)/(3))=0


Domain of the equation: 2)b!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-1(+1/2)b-(+b-1/3)+14/3=0

We multiply parentheses

-b^2-(+b-1/3)+14/3=0

We get rid of parentheses

-b^2-b+1/3+14/3=0

We multiply all the terms by the denominator


-b^2*3-b*3+1+14=0

We add all the numbers together, and all the variables

-b^2*3-b*3+15=0

Wy multiply elements

-3b^2-3b+15=0

a = -3; b = -3; c = +15;
Δ = b2-4ac
Δ = -32-4·(-3)·15
Δ = 189
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{21}}{2*-3}=\frac{3-3\sqrt{21}}{-6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{21}}{2*-3}=\frac{3+3\sqrt{21}}{-6}
$