2/a+7=8+1a

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

2/a+7=8+1a

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/a-a-8+7=0

We multiply all the terms by the denominator


-a*a-8*a+7*a+2=0

We add all the numbers together, and all the variables

-1a-a*a+2=0

Wy multiply elements

-1a^2-1a+2=0

a = -1; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*-1}=\frac{-2}{-2}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*-1}=\frac{4}{-2}
=-2
$