-2n(n+7)=15

Solution for -2n(n+7)=15 equation:

-2n(n+7)=15

We move all terms to the left:

-2n(n+7)-(15)=0

We multiply parentheses

-2n^2-14n-15=0

a = -2; b = -14; c = -15;
Δ = b2-4ac
Δ = -142-4·(-2)·(-15)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{19}}{2*-2}=\frac{14-2\sqrt{19}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{19}}{2*-2}=\frac{14+2\sqrt{19}}{-4}
$