(2n+7)(3n+4)=0

Solution for (2n+7)(3n+4)=0 equation:

(2n+7)(3n+4)=0

We multiply parentheses ..

(+6n^2+8n+21n+28)=0

We get rid of parentheses

6n^2+8n+21n+28=0

We add all the numbers together, and all the variables

6n^2+29n+28=0

a = 6; b = 29; c = +28;
Δ = b2-4ac
Δ = 292-4·6·28
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-13}{2*6}=\frac{-42}{12}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+13}{2*6}=\frac{-16}{12}
=-1+1/3
$