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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·(-2)·4
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{89}}{2*-2}=\frac{18-2\sqrt{89}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{89}}{2*-2}=\frac{18+2\sqrt{89}}{-4}
$