7-8/3b=-5+b

Solution for 7-8/3b=-5+b equation:

7-8/3b=-5+b

We move all terms to the left:

7-8/3b-(-5+b)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

-8/3b-(b-5)+7=0

We get rid of parentheses

-8/3b-b+5+7=0

We multiply all the terms by the denominator


-b*3b+5*3b+7*3b-8=0

Wy multiply elements

-3b^2+15b+21b-8=0

We add all the numbers together, and all the variables

-3b^2+36b-8=0

a = -3; b = 36; c = -8;
Δ = b2-4ac
Δ = 362-4·(-3)·(-8)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-20\sqrt{3}}{2*-3}=\frac{-36-20\sqrt{3}}{-6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+20\sqrt{3}}{2*-3}=\frac{-36+20\sqrt{3}}{-6}
$