-4n(2n-7)=0

Solution for -4n(2n-7)=0 equation:

-4n(2n-7)=0

We multiply parentheses

-8n^2+28n=0

a = -8; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-8)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-8}=\frac{-56}{-16}
=3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-8}=\frac{0}{-16}
=0
$