5n^2+28n+12=-3

Solution for 5n^2+28n+12=-3 equation:

5n^2+28n+12=-3

We move all terms to the left:

5n^2+28n+12-(-3)=0

We add all the numbers together, and all the variables

5n^2+28n+15=0

a = 5; b = 28; c = +15;
Δ = b2-4ac
Δ = 282-4·5·15
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-22}{2*5}=\frac{-50}{10}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+22}{2*5}=\frac{-6}{10}
=-3/5
$