x=3x^2-5x+1

Solution for x=3x^2-5x+1 equation:

x=3x^2-5x+1

We move all terms to the left:

x-(3x^2-5x+1)=0

We get rid of parentheses

-3x^2+x+5x-1=0

We add all the numbers together, and all the variables

-3x^2+6x-1=0

a = -3; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-3)·(-1)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{6}}{2*-3}=\frac{-6-2\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{6}}{2*-3}=\frac{-6+2\sqrt{6}}{-6}
$