(-1/2b+-1)+3b=-1

Solution for (-1/2b+-1)+3b=-1 equation:

(-1/2b+-1)+3b=-1

We move all terms to the left:

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


Domain of the equation: 2b+-1)!=0

b∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6b^2-2b+2b-1=0

We add all the numbers together, and all the variables

6b^2-1=0

a = 6; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·6·(-1)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*6}=\frac{0-2\sqrt{6}}{12}
=-\frac{2\sqrt{6}}{12}
=-\frac{\sqrt{6}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*6}=\frac{0+2\sqrt{6}}{12}
=\frac{2\sqrt{6}}{12}
=\frac{\sqrt{6}}{6}
$