0=k^2-14k+13

Solution for 0=k^2-14k+13 equation:

0=k^2-14k+13

We move all terms to the left:

0-(k^2-14k+13)=0

We add all the numbers together, and all the variables

-(k^2-14k+13)=0

We get rid of parentheses

-k^2+14k-13=0

We add all the numbers together, and all the variables

-1k^2+14k-13=0

a = -1; b = 14; c = -13;
Δ = b2-4ac
Δ = 142-4·(-1)·(-13)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-12}{2*-1}=\frac{-26}{-2}
=+13
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+12}{2*-1}=\frac{-2}{-2}
=1
$