3/a-8=7/2a+1

Solution for 3/a-8=7/2a+1 equation:

3/a-8=7/2a+1

We move all terms to the left:

3/a-8-(7/2a+1)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 2a+1)!=0

a∈R


We get rid of parentheses

3/a-7/2a-1-8=0

We calculate fractions


6a/2a^2+(-7a)/2a^2-1-8=0

We add all the numbers together, and all the variables

6a/2a^2+(-7a)/2a^2-9=0

We multiply all the terms by the denominator


6a+(-7a)-9*2a^2=0

Wy multiply elements

-18a^2+6a+(-7a)=0

We get rid of parentheses

-18a^2+6a-7a=0

We add all the numbers together, and all the variables

-18a^2-1a=0

a = -18; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-18)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-18}=\frac{0}{-36}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-18}=\frac{2}{-36}
=-1/18
$