2n(5n-2)=2n+12

Solution for 2n(5n-2)=2n+12 equation:

2n(5n-2)=2n+12

We move all terms to the left:

2n(5n-2)-(2n+12)=0

We multiply parentheses

10n^2-4n-(2n+12)=0

We get rid of parentheses

10n^2-4n-2n-12=0

We add all the numbers together, and all the variables

10n^2-6n-12=0

a = 10; b = -6; c = -12;
Δ = b2-4ac
Δ = -62-4·10·(-12)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{129}}{2*10}=\frac{6-2\sqrt{129}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{129}}{2*10}=\frac{6+2\sqrt{129}}{20}
$