2(5n^2)+10n-46)=0

Solution for 2(5n^2)+10n-46)=0 equation:

2(5n^2)+10n-46)=0

We add all the numbers together, and all the variables

25n^2+10n=0

a = 25; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·25·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*25}=\frac{-20}{50}
=-2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*25}=\frac{0}{50}
=0
$