5n(7n+8)=0

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

5n(7n+8)=0

We multiply parentheses

35n^2+40n=0

a = 35; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·35·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*35}=\frac{-80}{70}
=-1+1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*35}=\frac{0}{70}
=0
$