0=5x^2-6x+1

Solution for 0=5x^2-6x+1 equation:

0=5x^2-6x+1

We move all terms to the left:

0-(5x^2-6x+1)=0

We add all the numbers together, and all the variables

-(5x^2-6x+1)=0

We get rid of parentheses

-5x^2+6x-1=0

a = -5; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-5)·(-1)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4}{2*-5}=\frac{-2}{-10}
=1/5
$