-5n^2+4n+10=0

Solution for -5n^2+4n+10=0 equation:

-5n^2+4n+10=0

a = -5; b = 4; c = +10;
Δ = b2-4ac
Δ = 42-4·(-5)·10
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{6}}{2*-5}=\frac{-4-6\sqrt{6}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{6}}{2*-5}=\frac{-4+6\sqrt{6}}{-10}
$