-6.6+-4.1b=75+5/3b

Solution for -6.6+-4.1b=75+5/3b equation:

-6.6+-4.1b=75+5/3b

We move all terms to the left:

-6.6+-4.1b-(75+5/3b)=0


Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-4.1b-(5/3b+75)-6.6+=0

We add all the numbers together, and all the variables

-4.1b-(5/3b+75)=0

We get rid of parentheses

-4.1b-5/3b-75=0

We multiply all the terms by the denominator


-(4.1b)*3b-75*3b-5=0

We add all the numbers together, and all the variables

-(+4.1b)*3b-75*3b-5=0

We multiply parentheses

-12b^2-75*3b-5=0

Wy multiply elements

-12b^2-225b-5=0

a = -12; b = -225; c = -5;
Δ = b2-4ac
Δ = -2252-4·(-12)·(-5)
Δ = 50385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-225)-\sqrt{50385}}{2*-12}=\frac{225-\sqrt{50385}}{-24}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+\sqrt{50385}}{2*-12}=\frac{225+\sqrt{50385}}{-24}
$