x^2=13x+12=0

Solution for x^2=13x+12=0 equation:

x^2=13x+12=0

We move all terms to the left:

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

We get rid of parentheses

x^2-13x-12=0

a = 1; b = -13; c = -12;
Δ = b2-4ac
Δ = -132-4·1·(-12)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{217}}{2*1}=\frac{13-\sqrt{217}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{217}}{2*1}=\frac{13+\sqrt{217}}{2}
$