3/2b=8-2b

Solution for 3/2b=8-2b equation:

3/2b=8-2b

We move all terms to the left:

3/2b-(8-2b)=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-(-2b+8)=0

We get rid of parentheses

3/2b+2b-8=0

We multiply all the terms by the denominator


2b*2b-8*2b+3=0

Wy multiply elements

4b^2-16b+3=0

a = 4; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·4·3
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{13}}{2*4}=\frac{16-4\sqrt{13}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{13}}{2*4}=\frac{16+4\sqrt{13}}{8}
$