60n^2+234n+84=0

Solution for 60n^2+234n+84=0 equation:

60n^2+234n+84=0

a = 60; b = 234; c = +84;
Δ = b2-4ac
Δ = 2342-4·60·84
Δ = 34596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34596}=186$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-186}{2*60}=\frac{-420}{120}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+186}{2*60}=\frac{-48}{120}
=-2/5
$