3/2b+5+3/2b=12+3b

Solution for 3/2b+5+3/2b=12+3b equation:

3/2b+5+3/2b=12+3b

We move all terms to the left:

3/2b+5+3/2b-(12+3b)=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+3/2b-(3b+12)+5=0

We get rid of parentheses

3/2b+3/2b-3b-12+5=0

We multiply all the terms by the denominator


-3b*2b-12*2b+5*2b+3+3=0

We add all the numbers together, and all the variables

-3b*2b-12*2b+5*2b+6=0

Wy multiply elements

-6b^2-24b+10b+6=0

We add all the numbers together, and all the variables

-6b^2-14b+6=0

a = -6; b = -14; c = +6;
Δ = b2-4ac
Δ = -142-4·(-6)·6
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{85}}{2*-6}=\frac{14-2\sqrt{85}}{-12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{85}}{2*-6}=\frac{14+2\sqrt{85}}{-12}
$