2/3b+5=02-b

Solution for 2/3b+5=02-b equation:

2/3b+5=02-b

We move all terms to the left:

2/3b+5-(02-b)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

2/3b-(-1b+2)+5=0

We get rid of parentheses

2/3b+1b-2+5=0

We multiply all the terms by the denominator


1b*3b-2*3b+5*3b+2=0

Wy multiply elements

3b^2-6b+15b+2=0

We add all the numbers together, and all the variables

3b^2+9b+2=0

a = 3; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·3·2
Δ = 57
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{-(9)-\sqrt{57}}{2*3}=\frac{-9-\sqrt{57}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{57}}{2*3}=\frac{-9+\sqrt{57}}{6}
$