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

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

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

We move all terms to the left:

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


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

b∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


-(+b^2+1+3b*2*2)+1*2*2)=0

We add all the numbers together, and all the variables

-(+b^2+1+3b*2*2)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

Wy multiply elements

-1b^2-12b*2-1=0

Wy multiply elements

-1b^2-24b-1=0

a = -1; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·(-1)·(-1)
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{143}}{2*-1}=\frac{24-2\sqrt{143}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{143}}{2*-1}=\frac{24+2\sqrt{143}}{-2}
$