x*(x+7)=408

Solution for x*(x+7)=408 equation:

x(x+7)=408

We move all terms to the left:

x(x+7)-(408)=0

We multiply parentheses

x^2+7x-408=0

a = 1; b = 7; c = -408;
Δ = b2-4ac
Δ = 72-4·1·(-408)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-41}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+41}{2*1}=\frac{34}{2}
=17
$