(7n+2)(5n-4)=0

Solution for (7n+2)(5n-4)=0 equation:

(7n+2)(5n-4)=0

We multiply parentheses ..

(+35n^2-28n+10n-8)=0

We get rid of parentheses

35n^2-28n+10n-8=0

We add all the numbers together, and all the variables

35n^2-18n-8=0

a = 35; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·35·(-8)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-38}{2*35}=\frac{-20}{70}
=-2/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+38}{2*35}=\frac{56}{70}
=4/5
$