10n^2-65n=35=0

Solution for 10n^2-65n=35=0 equation:

10n^2-65n=35=0

We move all terms to the left:

10n^2-65n-(35)=0

a = 10; b = -65; c = -35;
Δ = b2-4ac
Δ = -652-4·10·(-35)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-75}{2*10}=\frac{-10}{20}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+75}{2*10}=\frac{140}{20}
=7
$