6n^2+11n=17

Solution for 6n^2+11n=17 equation:

6n^2+11n=17

We move all terms to the left:

6n^2+11n-(17)=0

a = 6; b = 11; c = -17;
Δ = b2-4ac
Δ = 112-4·6·(-17)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-23}{2*6}=\frac{-34}{12}
=-2+5/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+23}{2*6}=\frac{12}{12}
=1
$