x^2-13x-12=42

Solution for x^2-13x-12=42 equation:

x^2-13x-12=42

We move all terms to the left:

x^2-13x-12-(42)=0

We add all the numbers together, and all the variables

x^2-13x-54=0

a = 1; b = -13; c = -54;
Δ = b2-4ac
Δ = -132-4·1·(-54)
Δ = 385
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{385}}{2*1}=\frac{13-\sqrt{385}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{385}}{2*1}=\frac{13+\sqrt{385}}{2}
$