11n2+69n-52=0

Solution for 11n2+69n-52=0 equation:

11n^2+69n-52=0

a = 11; b = 69; c = -52;
Δ = b2-4ac
Δ = 692-4·11·(-52)
Δ = 7049
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{-(69)-\sqrt{7049}}{2*11}=\frac{-69-\sqrt{7049}}{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+\sqrt{7049}}{2*11}=\frac{-69+\sqrt{7049}}{22}
$