n(n+7)=42

Solution for n(n+7)=42 equation:

n(n+7)=42

We move all terms to the left:

n(n+7)-(42)=0

We multiply parentheses

n^2+7n-42=0

a = 1; b = 7; c = -42;
Δ = b2-4ac
Δ = 72-4·1·(-42)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{217}}{2*1}=\frac{-7-\sqrt{217}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{217}}{2*1}=\frac{-7+\sqrt{217}}{2}
$