3n^2-17n-11n=-5

Solution for 3n^2-17n-11n=-5 equation:

3n^2-17n-11n=-5

We move all terms to the left:

3n^2-17n-11n-(-5)=0

We add all the numbers together, and all the variables

3n^2-28n+5=0

a = 3; b = -28; c = +5;
Δ = b2-4ac
Δ = -282-4·3·5
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{181}}{2*3}=\frac{28-2\sqrt{181}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{181}}{2*3}=\frac{28+2\sqrt{181}}{6}
$