6n^2-10n-16=5

Solution for 6n^2-10n-16=5 equation:

6n^2-10n-16=5

We move all terms to the left:

6n^2-10n-16-(5)=0

We add all the numbers together, and all the variables

6n^2-10n-21=0

a = 6; b = -10; c = -21;
Δ = b2-4ac
Δ = -102-4·6·(-21)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{151}}{2*6}=\frac{10-2\sqrt{151}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{151}}{2*6}=\frac{10+2\sqrt{151}}{12}
$