5n^2+3n-1022=0

Solution for 5n^2+3n-1022=0 equation:

5n^2+3n-1022=0

a = 5; b = 3; c = -1022;
Δ = b2-4ac
Δ = 32-4·5·(-1022)
Δ = 20449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20449}=143$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-143}{2*5}=\frac{-146}{10}
=-14+3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+143}{2*5}=\frac{140}{10}
=14
$