10n^2-65n-75=0

Solution for 10n^2-65n-75=0 equation:

10n^2-65n-75=0

a = 10; b = -65; c = -75;
Δ = b2-4ac
Δ = -652-4·10·(-75)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-85}{2*10}=\frac{-20}{20}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+85}{2*10}=\frac{150}{20}
=7+1/2
$