(2n-1)(n+6)=11

Solution for (2n-1)(n+6)=11 equation:

(2n-1)(n+6)=11

We move all terms to the left:

(2n-1)(n+6)-(11)=0

We multiply parentheses ..

(+2n^2+12n-1n-6)-11=0

We get rid of parentheses

2n^2+12n-1n-6-11=0

We add all the numbers together, and all the variables

2n^2+11n-17=0

a = 2; b = 11; c = -17;
Δ = b2-4ac
Δ = 112-4·2·(-17)
Δ = 257
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{257}}{2*2}=\frac{-11-\sqrt{257}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{257}}{2*2}=\frac{-11+\sqrt{257}}{4}
$