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

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

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

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: a-1)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

18a^2+5a=0

a = 18; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·18·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*18}=\frac{-10}{36}
=-5/18
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*18}=\frac{0}{36}
=0
$