12n^2-14n-37=6n^2-12n-9

Solution for 12n^2-14n-37=6n^2-12n-9 equation:

12n^2-14n-37=6n^2-12n-9

We move all terms to the left:

12n^2-14n-37-(6n^2-12n-9)=0

We get rid of parentheses

12n^2-6n^2-14n+12n+9-37=0

We add all the numbers together, and all the variables

6n^2-2n-28=0

a = 6; b = -2; c = -28;
Δ = b2-4ac
Δ = -22-4·6·(-28)
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{-(-2)-26}{2*6}=\frac{-24}{12}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+26}{2*6}=\frac{28}{12}
=2+1/3
$