31n(X+2)=15

Solution for 31n(X+2)=15 equation:

31n(n+2)=15

We move all terms to the left:

31n(n+2)-(15)=0

We multiply parentheses

31n^2+62n-15=0

a = 31; b = 62; c = -15;
Δ = b2-4ac
Δ = 622-4·31·(-15)
Δ = 5704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5704}=\sqrt{4*1426}=\sqrt{4}*\sqrt{1426}=2\sqrt{1426}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{1426}}{2*31}=\frac{-62-2\sqrt{1426}}{62}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{1426}}{2*31}=\frac{-62+2\sqrt{1426}}{62}
$