4n-2n=-5n(2n-8)

Solution for 4n-2n=-5n(2n-8) equation:

4n-2n=-5n(2n-8)

We move all terms to the left:

4n-2n-(-5n(2n-8))=0

We add all the numbers together, and all the variables

2n-(-5n(2n-8))=0


We calculate terms in parentheses: -(-5n(2n-8)), so:

-5n(2n-8)

We multiply parentheses

-10n^2+40n

Back to the equation:

-(-10n^2+40n)


We get rid of parentheses

10n^2-40n+2n=0

We add all the numbers together, and all the variables

10n^2-38n=0

a = 10; b = -38; c = 0;
Δ = b2-4ac
Δ = -382-4·10·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38}{2*10}=\frac{0}{20}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38}{2*10}=\frac{76}{20}
=3+4/5
$