35n^2+110n-80=0

Solution for 35n^2+110n-80=0 equation:

35n^2+110n-80=0

a = 35; b = 110; c = -80;
Δ = b2-4ac
Δ = 1102-4·35·(-80)
Δ = 23300
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:

$\sqrt{\Delta}=\sqrt{23300}=\sqrt{100*233}=\sqrt{100}*\sqrt{233}=10\sqrt{233}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-10\sqrt{233}}{2*35}=\frac{-110-10\sqrt{233}}{70}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+10\sqrt{233}}{2*35}=\frac{-110+10\sqrt{233}}{70}
$