1/3b+8-0.5b=-4

Solution for 1/3b+8-0.5b=-4 equation:

1/3b+8-0.5b=-4

We move all terms to the left:

1/3b+8-0.5b-(-4)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

-0.5b+1/3b+12=0

We multiply all the terms by the denominator


-(0.5b)*3b+12*3b+1=0

We add all the numbers together, and all the variables

-(+0.5b)*3b+12*3b+1=0

We multiply parentheses

-0b^2+12*3b+1=0

Wy multiply elements

-0b^2+36b+1=0

We add all the numbers together, and all the variables

-1b^2+36b+1=0

a = -1; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-1)·1
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-10\sqrt{13}}{2*-1}=\frac{-36-10\sqrt{13}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+10\sqrt{13}}{2*-1}=\frac{-36+10\sqrt{13}}{-2}
$