(n)=12n2+-11n=15

Solution for (n)=12n2+-11n=15 equation:

(n)=12n^2+-11n=15

We move all terms to the left:

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

We use the square of the difference formula

n-(12n^2-11n)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-12n^2+12n=0

a = -12; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-12)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-12}=\frac{-24}{-24}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-12}=\frac{0}{-24}
=0
$