b(2/3)=1/3

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

b(2/3)=1/3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

2b^2-1/3=0

We multiply all the terms by the denominator


2b^2*3-1=0

Wy multiply elements

6b^2-1=0

a = 6; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·6·(-1)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*6}=\frac{0-2\sqrt{6}}{12}
=-\frac{2\sqrt{6}}{12}
=-\frac{\sqrt{6}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*6}=\frac{0+2\sqrt{6}}{12}
=\frac{2\sqrt{6}}{12}
=\frac{\sqrt{6}}{6}
$