7n(-8n+2)=0

Solution for 7n(-8n+2)=0 equation:

7n(-8n+2)=0

We multiply parentheses

-56n^2+14n=0

a = -56; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-56)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-56}=\frac{-28}{-112}
=1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-56}=\frac{0}{-112}
=0
$