31/3=b2/3

Solution for 31/3=b2/3 equation:

31/3=b2/3

We move all terms to the left:

31/3-(b2/3)=0

We add all the numbers together, and all the variables

-(+b2/3)+31/3=0

We get rid of parentheses

-b2/3+31/3=0

We multiply all the terms by the denominator


-b2+31=0

We add all the numbers together, and all the variables

-1b^2+31=0

a = -1; b = 0; c = +31;
Δ = b2-4ac
Δ = 02-4·(-1)·31
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{31}}{2*-1}=\frac{0-2\sqrt{31}}{-2}
=-\frac{2\sqrt{31}}{-2}
=-\frac{\sqrt{31}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{31}}{2*-1}=\frac{0+2\sqrt{31}}{-2}
=\frac{2\sqrt{31}}{-2}
=\frac{\sqrt{31}}{-1}
$