2/3b+b=12/3b

Solution for 2/3b+b=12/3b equation:

2/3b+b=12/3b

We move all terms to the left:

2/3b+b-(12/3b)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

2/3b+b-(+12/3b)=0

We add all the numbers together, and all the variables

b+2/3b-(+12/3b)=0

We get rid of parentheses

b+2/3b-12/3b=0

We multiply all the terms by the denominator


b*3b+2-12=0

We add all the numbers together, and all the variables

b*3b-10=0

Wy multiply elements

3b^2-10=0

a = 3; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·3·(-10)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*3}=\frac{0-2\sqrt{30}}{6}
=-\frac{2\sqrt{30}}{6}
=-\frac{\sqrt{30}}{3}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*3}=\frac{0+2\sqrt{30}}{6}
=\frac{2\sqrt{30}}{6}
=\frac{\sqrt{30}}{3}
$