0=x^2-51x+1

Solution for 0=x^2-51x+1 equation:

0=x^2-51x+1

We move all terms to the left:

0-(x^2-51x+1)=0

We add all the numbers together, and all the variables

-(x^2-51x+1)=0

We get rid of parentheses

-x^2+51x-1=0

We add all the numbers together, and all the variables

-1x^2+51x-1=0

a = -1; b = 51; c = -1;
Δ = b2-4ac
Δ = 512-4·(-1)·(-1)
Δ = 2597
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:

$\sqrt{\Delta}=\sqrt{2597}=\sqrt{49*53}=\sqrt{49}*\sqrt{53}=7\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-7\sqrt{53}}{2*-1}=\frac{-51-7\sqrt{53}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+7\sqrt{53}}{2*-1}=\frac{-51+7\sqrt{53}}{-2}
$