x^2+9x+13=4

Solution for x^2+9x+13=4 equation:

x^2+9x+13=4

We move all terms to the left:

x^2+9x+13-(4)=0

We add all the numbers together, and all the variables

x^2+9x+9=0

a = 1; b = 9; c = +9;
Δ = b2-4ac
Δ = 92-4·1·9
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{5}}{2*1}=\frac{-9-3\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{5}}{2*1}=\frac{-9+3\sqrt{5}}{2}
$