5n^2+20n-2022=0

Solution for 5n^2+20n-2022=0 equation:

5n^2+20n-2022=0

a = 5; b = 20; c = -2022;
Δ = b2-4ac
Δ = 202-4·5·(-2022)
Δ = 40840
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:

$\sqrt{\Delta}=\sqrt{40840}=\sqrt{4*10210}=\sqrt{4}*\sqrt{10210}=2\sqrt{10210}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{10210}}{2*5}=\frac{-20-2\sqrt{10210}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{10210}}{2*5}=\frac{-20+2\sqrt{10210}}{10}
$