2=x^2+13x+38

Solution for 2=x^2+13x+38 equation:

2=x^2+13x+38

We move all terms to the left:

2-(x^2+13x+38)=0

We get rid of parentheses

-x^2-13x-38+2=0

We add all the numbers together, and all the variables

-1x^2-13x-36=0

a = -1; b = -13; c = -36;
Δ = b2-4ac
Δ = -132-4·(-1)·(-36)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*-1}=\frac{8}{-2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*-1}=\frac{18}{-2}
=-9
$