3-1/2b=-1/3b-7

Solution for 3-1/2b=-1/3b-7 equation:

3-1/2b=-1/3b-7

We move all terms to the left:

3-1/2b-(-1/3b-7)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 3b-7)!=0

b∈R


We get rid of parentheses

-1/2b+1/3b+7+3=0

We calculate fractions


(-3b)/6b^2+2b/6b^2+7+3=0

We add all the numbers together, and all the variables

(-3b)/6b^2+2b/6b^2+10=0

We multiply all the terms by the denominator


(-3b)+2b+10*6b^2=0

We add all the numbers together, and all the variables

2b+(-3b)+10*6b^2=0

Wy multiply elements

60b^2+2b+(-3b)=0

We get rid of parentheses

60b^2+2b-3b=0

We add all the numbers together, and all the variables

60b^2-1b=0

a = 60; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·60·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*60}=\frac{0}{120}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*60}=\frac{2}{120}
=1/60
$