1/a=a-1

Solution for 1/a=a-1 equation:

1/a=a-1

We move all terms to the left:

1/a-(a-1)=0


Domain of the equation: a!=0

a∈R


We get rid of parentheses

1/a-a+1=0

We multiply all the terms by the denominator


-a*a+1*a+1=0

We add all the numbers together, and all the variables

a-a*a+1=0

Wy multiply elements

-1a^2+a+1=0

a = -1; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-1)·1
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{5}}{2*-1}=\frac{-1-\sqrt{5}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*-1}=\frac{-1+\sqrt{5}}{-2}
$