3n^2+21n+37=7

Solution for 3n^2+21n+37=7 equation:

3n^2+21n+37=7

We move all terms to the left:

3n^2+21n+37-(7)=0

We add all the numbers together, and all the variables

3n^2+21n+30=0

a = 3; b = 21; c = +30;
Δ = b2-4ac
Δ = 212-4·3·30
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-9}{2*3}=\frac{-30}{6}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+9}{2*3}=\frac{-12}{6}
=-2
$