(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

Wy multiply elements

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

Wy multiply elements

b^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}
$