4n2-16n=48

Solution for 4n2-16n=48 equation:

4n^2-16n=48

We move all terms to the left:

4n^2-16n-(48)=0

a = 4; b = -16; c = -48;
Δ = b2-4ac
Δ = -162-4·4·(-48)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-32}{2*4}=\frac{-16}{8}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+32}{2*4}=\frac{48}{8}
=6
$