3/2b+b+1/2b=15+2b

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

3/2b+b+1/2b=15+2b

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·(-2)·4
Δ = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{233}}{2*-2}=\frac{30-2\sqrt{233}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{233}}{2*-2}=\frac{30+2\sqrt{233}}{-4}
$