(3)/(2)b+6+(1)/(2)b=15+2b

Solution for (3)/(2)b+6+(1)/(2)b=15+2b equation:

(3)/(2)b+6+(1)/(2)b=15+2b

We move all terms to the left:

(3)/(2)b+6+(1)/(2)b-(15+2b)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

3/2b+1/2b-(2b+15)+6=0

We get rid of parentheses

3/2b+1/2b-2b-15+6=0

We multiply all the terms by the denominator


-2b*2b-15*2b+6*2b+3+1=0

We add all the numbers together, and all the variables

-2b*2b-15*2b+6*2b+4=0

Wy multiply elements

-4b^2-30b+12b+4=0

We add all the numbers together, and all the variables

-4b^2-18b+4=0

a = -4; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·(-4)·4
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{97}}{2*-4}=\frac{18-2\sqrt{97}}{-8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{97}}{2*-4}=\frac{18+2\sqrt{97}}{-8}
$