5n2+19n-68=-2

Solution for 5n2+19n-68=-2 equation:

5n^2+19n-68=-2

We move all terms to the left:

5n^2+19n-68-(-2)=0

We add all the numbers together, and all the variables

5n^2+19n-66=0

a = 5; b = 19; c = -66;
Δ = b2-4ac
Δ = 192-4·5·(-66)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-41}{2*5}=\frac{-60}{10}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+41}{2*5}=\frac{22}{10}
=2+1/5
$