(6n+7)(3n-8)=0

Solution for (6n+7)(3n-8)=0 equation:

(6n+7)(3n-8)=0

We multiply parentheses ..

(+18n^2-48n+21n-56)=0

We get rid of parentheses

18n^2-48n+21n-56=0

We add all the numbers together, and all the variables

18n^2-27n-56=0

a = 18; b = -27; c = -56;
Δ = b2-4ac
Δ = -272-4·18·(-56)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-69}{2*18}=\frac{-42}{36}
=-1+1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+69}{2*18}=\frac{96}{36}
=2+2/3
$