-5n(4n-2)=-2(3+6n)

Solution for -5n(4n-2)=-2(3+6n) equation:

-5n(4n-2)=-2(3+6n)

We move all terms to the left:

-5n(4n-2)-(-2(3+6n))=0

We add all the numbers together, and all the variables

-5n(4n-2)-(-2(6n+3))=0

We multiply parentheses

-20n^2+10n-(-2(6n+3))=0


We calculate terms in parentheses: -(-2(6n+3)), so:

-2(6n+3)

We multiply parentheses

-12n-6

Back to the equation:

-(-12n-6)


We get rid of parentheses

-20n^2+10n+12n+6=0

We add all the numbers together, and all the variables

-20n^2+22n+6=0

a = -20; b = 22; c = +6;
Δ = b2-4ac
Δ = 222-4·(-20)·6
Δ = 964
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:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{241}}{2*-20}=\frac{-22-2\sqrt{241}}{-40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{241}}{2*-20}=\frac{-22+2\sqrt{241}}{-40}
$