5=b-2/3b

Solution for 5=b-2/3b equation:

5=b-2/3b

We move all terms to the left:

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


Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-(+b-2/3b)+5=0

We get rid of parentheses

-b+2/3b+5=0

We multiply all the terms by the denominator


-b*3b+5*3b+2=0

Wy multiply elements

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

a = -3; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·(-3)·2
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{249}}{2*-3}=\frac{-15-\sqrt{249}}{-6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{249}}{2*-3}=\frac{-15+\sqrt{249}}{-6}
$