(11n+14)(7n+3)=0

Solution for (11n+14)(7n+3)=0 equation:

(11n+14)(7n+3)=0

We multiply parentheses ..

(+77n^2+33n+98n+42)=0

We get rid of parentheses

77n^2+33n+98n+42=0

We add all the numbers together, and all the variables

77n^2+131n+42=0

a = 77; b = 131; c = +42;
Δ = b2-4ac
Δ = 1312-4·77·42
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(131)-65}{2*77}=\frac{-196}{154}
=-1+3/11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(131)+65}{2*77}=\frac{-66}{154}
=-3/7
$