10*(1/a^2)-(1/a)-2=0

Solution for 10*(1/a^2)-(1/a)-2=0 equation:

10(1/a^2)-(1/a)-2=0


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

a!=0/1

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

10(1/a^2)-(+1/a)-2=0

We multiply parentheses

10a-(+1/a)-2=0

We get rid of parentheses

10a-1/a-2=0

We multiply all the terms by the denominator


10a*a-2*a-1=0

We add all the numbers together, and all the variables

-2a+10a*a-1=0

Wy multiply elements

10a^2-2a-1=0

a = 10; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·10·(-1)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11}}{2*10}=\frac{2-2\sqrt{11}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11}}{2*10}=\frac{2+2\sqrt{11}}{20}
$