-7/6(a)+13/4=-5/8(a)

Solution for -7/6(a)+13/4=-5/8(a) equation:

-7/6(a)+13/4=-5/8(a)

We move all terms to the left:

-7/6(a)+13/4-(-5/8(a))=0


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R



Domain of the equation: 8a)!=0

a!=0/1

a!=0

a∈R


We get rid of parentheses

-7/6a+5/8a+13/4=0

We calculate fractions


4992a^2/768a^2+(-896a)/768a^2+480a/768a^2=0

We multiply all the terms by the denominator


4992a^2+(-896a)+480a=0

We add all the numbers together, and all the variables

4992a^2+480a+(-896a)=0

We get rid of parentheses

4992a^2+480a-896a=0

We add all the numbers together, and all the variables

4992a^2-416a=0

a = 4992; b = -416; c = 0;
Δ = b2-4ac
Δ = -4162-4·4992·0
Δ = 173056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{173056}=416$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-416)-416}{2*4992}=\frac{0}{9984}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-416)+416}{2*4992}=\frac{832}{9984}
=1/12
$