2/3b+2+b=84

Solution for 2/3b+2+b=84 equation:

2/3b+2+b=84

We move all terms to the left:

2/3b+2+b-(84)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

b+2/3b-82=0

We multiply all the terms by the denominator


b*3b-82*3b+2=0

Wy multiply elements

3b^2-246b+2=0

a = 3; b = -246; c = +2;
Δ = b2-4ac
Δ = -2462-4·3·2
Δ = 60492
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:

$\sqrt{\Delta}=\sqrt{60492}=\sqrt{20164*3}=\sqrt{20164}*\sqrt{3}=142\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-246)-142\sqrt{3}}{2*3}=\frac{246-142\sqrt{3}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-246)+142\sqrt{3}}{2*3}=\frac{246+142\sqrt{3}}{6}
$