2a=(a^2-3a+1)

Solution for 2a=(a^2-3a+1) equation:

2a=(a^2-3a+1)

We move all terms to the left:

2a-((a^2-3a+1))=0


We calculate terms in parentheses: -((a^2-3a+1)), so:

(a^2-3a+1)

We get rid of parentheses

a^2-3a+1

Back to the equation:

-(a^2-3a+1)


We get rid of parentheses

-a^2+2a+3a-1=0

We add all the numbers together, and all the variables

-1a^2+5a-1=0

a = -1; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-1)·(-1)
Δ = 21
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{-(5)-\sqrt{21}}{2*-1}=\frac{-5-\sqrt{21}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{21}}{2*-1}=\frac{-5+\sqrt{21}}{-2}
$