2n(n+3)=n+12

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

2n(n+3)=n+12

We move all terms to the left:

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

We multiply parentheses

2n^2+6n-(n+12)=0

We get rid of parentheses

2n^2+6n-n-12=0

We add all the numbers together, and all the variables

2n^2+5n-12=0

a = 2; b = 5; c = -12;
Δ = b2-4ac
Δ = 52-4·2·(-12)
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*2}=\frac{-16}{4}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*2}=\frac{6}{4}
=1+1/2
$