x^2-9x-13=37

Solution for x^2-9x-13=37 equation:

x^2-9x-13=37

We move all terms to the left:

x^2-9x-13-(37)=0

We add all the numbers together, and all the variables

x^2-9x-50=0

a = 1; b = -9; c = -50;
Δ = b2-4ac
Δ = -92-4·1·(-50)
Δ = 281
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{-(-9)-\sqrt{281}}{2*1}=\frac{9-\sqrt{281}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{281}}{2*1}=\frac{9+\sqrt{281}}{2}
$