-31/2b-21/4b=-115/12

Solution for -31/2b-21/4b=-115/12 equation:

-31/2b-21/4b=-115/12

We move all terms to the left:

-31/2b-21/4b-(-115/12)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We get rid of parentheses

-31/2b-21/4b+115/12=0

We calculate fractions


3680b^2/96b^2+(-1488b)/96b^2+(-504b)/96b^2=0

We multiply all the terms by the denominator


3680b^2+(-1488b)+(-504b)=0

We get rid of parentheses

3680b^2-1488b-504b=0

We add all the numbers together, and all the variables

3680b^2-1992b=0

a = 3680; b = -1992; c = 0;
Δ = b2-4ac
Δ = -19922-4·3680·0
Δ = 3968064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3968064}=1992$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1992)-1992}{2*3680}=\frac{0}{7360}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1992)+1992}{2*3680}=\frac{3984}{7360}
=249/460
$