6n^2+102n+420=0

Solution for 6n^2+102n+420=0 equation:

6n^2+102n+420=0

a = 6; b = 102; c = +420;
Δ = b2-4ac
Δ = 1022-4·6·420
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-18}{2*6}=\frac{-120}{12}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+18}{2*6}=\frac{-84}{12}
=-7
$