x(13+x)=420

Solution for x(13+x)=420 equation:

x(13+x)=420

We move all terms to the left:

x(13+x)-(420)=0

We add all the numbers together, and all the variables

x(x+13)-420=0

We multiply parentheses

x^2+13x-420=0

a = 1; b = 13; c = -420;
Δ = b2-4ac
Δ = 132-4·1·(-420)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-43}{2*1}=\frac{-56}{2}
=-28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+43}{2*1}=\frac{30}{2}
=15
$