5n(3n-4)-2(4-3n)=0

Solution for 5n(3n-4)-2(4-3n)=0 equation:

5n(3n-4)-2(4-3n)=0

We add all the numbers together, and all the variables

5n(3n-4)-2(-3n+4)=0

We multiply parentheses

15n^2-20n+6n-8=0

We add all the numbers together, and all the variables

15n^2-14n-8=0

a = 15; b = -14; c = -8;
Δ = b2-4ac
Δ = -142-4·15·(-8)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-26}{2*15}=\frac{-12}{30}
=-2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*15}=\frac{40}{30}
=1+1/3
$