5n^2-8n-14=0

Solution for 5n^2-8n-14=0 equation:

5n^2-8n-14=0

a = 5; b = -8; c = -14;
Δ = b2-4ac
Δ = -82-4·5·(-14)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{86}}{2*5}=\frac{8-2\sqrt{86}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{86}}{2*5}=\frac{8+2\sqrt{86}}{10}
$