12n(n+2)=11n-3

Solution for 12n(n+2)=11n-3 equation:

12n(n+2)=11n-3

We move all terms to the left:

12n(n+2)-(11n-3)=0

We multiply parentheses

12n^2+24n-(11n-3)=0

We get rid of parentheses

12n^2+24n-11n+3=0

We add all the numbers together, and all the variables

12n^2+13n+3=0

a = 12; b = 13; c = +3;
Δ = b2-4ac
Δ = 132-4·12·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5}{2*12}=\frac{-18}{24}
=-3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*12}=\frac{-8}{24}
=-1/3
$