(2n-1)(3n+4)=0

Solution for (2n-1)(3n+4)=0 equation:

(2n-1)(3n+4)=0

We multiply parentheses ..

(+6n^2+8n-3n-4)=0

We get rid of parentheses

6n^2+8n-3n-4=0

We add all the numbers together, and all the variables

6n^2+5n-4=0

a = 6; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·6·(-4)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*6}=\frac{-16}{12}
=-1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*6}=\frac{6}{12}
=1/2
$