31n=12n^2-7

Solution for 31n=12n^2-7 equation:

31n=12n^2-7

We move all terms to the left:

31n-(12n^2-7)=0

We get rid of parentheses

-12n^2+31n+7=0

a = -12; b = 31; c = +7;
Δ = b2-4ac
Δ = 312-4·(-12)·7
Δ = 1297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{1297}}{2*-12}=\frac{-31-\sqrt{1297}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{1297}}{2*-12}=\frac{-31+\sqrt{1297}}{-24}
$