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

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

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

We multiply parentheses ..

(+28n^2+49n-32n-56)=0

We get rid of parentheses

28n^2+49n-32n-56=0

We add all the numbers together, and all the variables

28n^2+17n-56=0

a = 28; b = 17; c = -56;
Δ = b2-4ac
Δ = 172-4·28·(-56)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-81}{2*28}=\frac{-98}{56}
=-1+3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+81}{2*28}=\frac{64}{56}
=1+1/7
$