x2+13=14x

Solution for x2+13=14x equation:

x2+13=14x

We move all terms to the left:

x2+13-(14x)=0

We add all the numbers together, and all the variables

x^2-14x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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