6n^2+11n+2=5

Solution for 6n^2+11n+2=5 equation:

6n^2+11n+2=5

We move all terms to the left:

6n^2+11n+2-(5)=0

We add all the numbers together, and all the variables

6n^2+11n-3=0

a = 6; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·6·(-3)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{193}}{2*6}=\frac{-11-\sqrt{193}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{193}}{2*6}=\frac{-11+\sqrt{193}}{12}
$