x(x+3)=420

Solution for x(x+3)=420 equation:

x(x+3)=420

We move all terms to the left:

x(x+3)-(420)=0

We multiply parentheses

x^2+3x-420=0

a = 1; b = 3; c = -420;
Δ = b2-4ac
Δ = 32-4·1·(-420)
Δ = 1689
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{-(3)-\sqrt{1689}}{2*1}=\frac{-3-\sqrt{1689}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{1689}}{2*1}=\frac{-3+\sqrt{1689}}{2}
$