n^2+7n+12=5

Solution for n^2+7n+12=5 equation:

n^2+7n+12=5

We move all terms to the left:

n^2+7n+12-(5)=0

We add all the numbers together, and all the variables

n^2+7n+7=0

a = 1; b = 7; c = +7;
Δ = b2-4ac
Δ = 72-4·1·7
Δ = 21
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{21}}{2*1}=\frac{-7-\sqrt{21}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{21}}{2*1}=\frac{-7+\sqrt{21}}{2}
$