15=2/3b+b

Solution for 15=2/3b+b equation:

15=2/3b+b

We move all terms to the left:

15-(2/3b+b)=0


Domain of the equation: 3b+b)!=0

b∈R


We add all the numbers together, and all the variables

-(+b+2/3b)+15=0

We get rid of parentheses

-b-2/3b+15=0

We multiply all the terms by the denominator


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

Wy multiply elements

-3b^2+45b-2=0

a = -3; b = 45; c = -2;
Δ = b2-4ac
Δ = 452-4·(-3)·(-2)
Δ = 2001
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{-(45)-\sqrt{2001}}{2*-3}=\frac{-45-\sqrt{2001}}{-6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2001}}{2*-3}=\frac{-45+\sqrt{2001}}{-6}
$