10n^2-6n-35=0

Solution for 10n^2-6n-35=0 equation:

10n^2-6n-35=0

a = 10; b = -6; c = -35;
Δ = b2-4ac
Δ = -62-4·10·(-35)
Δ = 1436
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:

$\sqrt{\Delta}=\sqrt{1436}=\sqrt{4*359}=\sqrt{4}*\sqrt{359}=2\sqrt{359}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{359}}{2*10}=\frac{6-2\sqrt{359}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{359}}{2*10}=\frac{6+2\sqrt{359}}{20}
$