10n^2+31n-45=0

Solution for 10n^2+31n-45=0 equation:

10n^2+31n-45=0

a = 10; b = 31; c = -45;
Δ = b2-4ac
Δ = 312-4·10·(-45)
Δ = 2761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{2761}}{2*10}=\frac{-31-\sqrt{2761}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{2761}}{2*10}=\frac{-31+\sqrt{2761}}{20}
$