(2n+11)(3n+7)=0

Solution for (2n+11)(3n+7)=0 equation:

(2n+11)(3n+7)=0

We multiply parentheses ..

(+6n^2+14n+33n+77)=0

We get rid of parentheses

6n^2+14n+33n+77=0

We add all the numbers together, and all the variables

6n^2+47n+77=0

a = 6; b = 47; c = +77;
Δ = b2-4ac
Δ = 472-4·6·77
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-19}{2*6}=\frac{-66}{12}
=-5+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+19}{2*6}=\frac{-28}{12}
=-2+1/3
$