2/a+2+1/a+1+4/2a-5=0

Solution for 2/a+2+1/a+1+4/2a-5=0 equation:

2/a+2+1/a+1+4/2a-5=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


(2a+2)+4a-2*2a^2=0

We add all the numbers together, and all the variables

4a+(2a+2)-2*2a^2=0

Wy multiply elements

-4a^2+4a+(2a+2)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4a^2+6a+2=0

a = -4; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-4)·2
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*-4}=\frac{-6-2\sqrt{17}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*-4}=\frac{-6+2\sqrt{17}}{-8}
$