10n^2-12n-17=0

Solution for 10n^2-12n-17=0 equation:

10n^2-12n-17=0

a = 10; b = -12; c = -17;
Δ = b2-4ac
Δ = -122-4·10·(-17)
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{206}}{2*10}=\frac{12-2\sqrt{206}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{206}}{2*10}=\frac{12+2\sqrt{206}}{20}
$