4n^2-16n=23

Solution for 4n^2-16n=23 equation:

4n^2-16n=23

We move all terms to the left:

4n^2-16n-(23)=0

a = 4; b = -16; c = -23;
Δ = b2-4ac
Δ = -162-4·4·(-23)
Δ = 624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{39}}{2*4}=\frac{16-4\sqrt{39}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{39}}{2*4}=\frac{16+4\sqrt{39}}{8}
$