3/a+4=a-1/a

Solution for 3/a+4=a-1/a equation:

3/a+4=a-1/a

We move all terms to the left:

3/a+4-(a-1/a)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

3/a-(+a-1/a)+4=0

We get rid of parentheses

3/a-a+1/a+4=0

We multiply all the terms by the denominator


-a*a+4*a+3+1=0

We add all the numbers together, and all the variables

4a-a*a+4=0

Wy multiply elements

-1a^2+4a+4=0

a = -1; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-1)·4
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-1}=\frac{-4-4\sqrt{2}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-1}=\frac{-4+4\sqrt{2}}{-2}
$