x^2-13=12x

Solution for x^2-13=12x equation:

x^2-13=12x

We move all terms to the left:

x^2-13-(12x)=0

a = 1; b = -12; c = -13;
Δ = b2-4ac
Δ = -122-4·1·(-13)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-14}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+14}{2*1}=\frac{26}{2}
=13
$