-n(4n-7)=0

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

-n(4n-7)=0

We multiply parentheses

-4n^2+7n=0

a = -4; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-4)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-4}=\frac{-14}{-8}
=1+3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-4}=\frac{0}{-8}
=0
$