4a-1/a+4=-2a-1/a+2

Solution for 4a-1/a+4=-2a-1/a+2 equation:

4a-1/a+4=-2a-1/a+2

We move all terms to the left:

4a-1/a+4-(-2a-1/a+2)=0


Domain of the equation: a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2a+4a*a+2a*a=0

Wy multiply elements

4a^2+2a^2+2a=0

We add all the numbers together, and all the variables

6a^2+2a=0

a = 6; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·6·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*6}=\frac{-4}{12}
=-1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*6}=\frac{0}{12}
=0
$