(7n+4)(5n+8)=0

Solution for (7n+4)(5n+8)=0 equation:

(7n+4)(5n+8)=0

We multiply parentheses ..

(+35n^2+56n+20n+32)=0

We get rid of parentheses

35n^2+56n+20n+32=0

We add all the numbers together, and all the variables

35n^2+76n+32=0

a = 35; b = 76; c = +32;
Δ = b2-4ac
Δ = 762-4·35·32
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-36}{2*35}=\frac{-112}{70}
=-1+3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+36}{2*35}=\frac{-40}{70}
=-4/7
$