6(5n2+8)=1968

Solution for 6(5n2+8)=1968 equation:

6(5n^2+8)=1968

We move all terms to the left:

6(5n^2+8)-(1968)=0

We multiply parentheses

30n^2+48-1968=0

We add all the numbers together, and all the variables

30n^2-1920=0

a = 30; b = 0; c = -1920;
Δ = b2-4ac
Δ = 02-4·30·(-1920)
Δ = 230400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{230400}=480$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-480}{2*30}=\frac{-480}{60}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+480}{2*30}=\frac{480}{60}
=8
$