3n^2-16n=20=0

Solution for 3n^2-16n=20=0 equation:

3n^2-16n=20=0

We move all terms to the left:

3n^2-16n-(20)=0

a = 3; b = -16; c = -20;
Δ = b2-4ac
Δ = -162-4·3·(-20)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{31}}{2*3}=\frac{16-4\sqrt{31}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{31}}{2*3}=\frac{16+4\sqrt{31}}{6}
$