7n(5n-8)=0

Solution for 7n(5n-8)=0 equation:

7n(5n-8)=0

We multiply parentheses

35n^2-56n=0

a = 35; b = -56; c = 0;
Δ = b2-4ac
Δ = -562-4·35·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-56}{2*35}=\frac{0}{70}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+56}{2*35}=\frac{112}{70}
=1+3/5
$