13x+x(x+4)=5

Solution for 13x+x(x+4)=5 equation:

13x+x(x+4)=5

We move all terms to the left:

13x+x(x+4)-(5)=0

We multiply parentheses

x^2+13x+4x-5=0

We add all the numbers together, and all the variables

x^2+17x-5=0

a = 1; b = 17; c = -5;
Δ = b2-4ac
Δ = 172-4·1·(-5)
Δ = 309
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{-(17)-\sqrt{309}}{2*1}=\frac{-17-\sqrt{309}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{309}}{2*1}=\frac{-17+\sqrt{309}}{2}
$