5n2-32n-35=0

Solution for 5n2-32n-35=0 equation:

5n^2-32n-35=0

a = 5; b = -32; c = -35;
Δ = b2-4ac
Δ = -322-4·5·(-35)
Δ = 1724
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:

$\sqrt{\Delta}=\sqrt{1724}=\sqrt{4*431}=\sqrt{4}*\sqrt{431}=2\sqrt{431}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{431}}{2*5}=\frac{32-2\sqrt{431}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{431}}{2*5}=\frac{32+2\sqrt{431}}{10}
$