11n^2+8n-15=0

Solution for 11n^2+8n-15=0 equation:

11n^2+8n-15=0

a = 11; b = 8; c = -15;
Δ = b2-4ac
Δ = 82-4·11·(-15)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{181}}{2*11}=\frac{-8-2\sqrt{181}}{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{181}}{2*11}=\frac{-8+2\sqrt{181}}{22}
$