-5n^2+6n+12=2

Solution for -5n^2+6n+12=2 equation:

-5n^2+6n+12=2

We move all terms to the left:

-5n^2+6n+12-(2)=0

We add all the numbers together, and all the variables

-5n^2+6n+10=0

a = -5; b = 6; c = +10;
Δ = b2-4ac
Δ = 62-4·(-5)·10
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{59}}{2*-5}=\frac{-6-2\sqrt{59}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{59}}{2*-5}=\frac{-6+2\sqrt{59}}{-10}
$