n^2+7n+4=82

Solution for n^2+7n+4=82 equation:

n^2+7n+4=82

We move all terms to the left:

n^2+7n+4-(82)=0

We add all the numbers together, and all the variables

n^2+7n-78=0

a = 1; b = 7; c = -78;
Δ = b2-4ac
Δ = 72-4·1·(-78)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-19}{2*1}=\frac{-26}{2}
=-13
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+19}{2*1}=\frac{12}{2}
=6
$