7n^2-10n-5=0

Solution for 7n^2-10n-5=0 equation:

7n^2-10n-5=0

a = 7; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·7·(-5)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{15}}{2*7}=\frac{10-4\sqrt{15}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{15}}{2*7}=\frac{10+4\sqrt{15}}{14}
$