-2n(2n-3)=-14

Solution for -2n(2n-3)=-14 equation:

-2n(2n-3)=-14

We move all terms to the left:

-2n(2n-3)-(-14)=0

We add all the numbers together, and all the variables

-2n(2n-3)+14=0

We multiply parentheses

-4n^2+6n+14=0

a = -4; b = 6; c = +14;
Δ = b2-4ac
Δ = 62-4·(-4)·14
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{65}}{2*-4}=\frac{-6-2\sqrt{65}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{65}}{2*-4}=\frac{-6+2\sqrt{65}}{-8}
$