-4n=-7n(1-2n)

Solution for -4n=-7n(1-2n) equation:

-4n=-7n(1-2n)

We move all terms to the left:

-4n-(-7n(1-2n))=0

We add all the numbers together, and all the variables

-4n-(-7n(-2n+1))=0


We calculate terms in parentheses: -(-7n(-2n+1)), so:

-7n(-2n+1)

We multiply parentheses

14n^2-7n

Back to the equation:

-(14n^2-7n)


We get rid of parentheses

-14n^2-4n+7n=0

We add all the numbers together, and all the variables

-14n^2+3n=0

a = -14; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-14)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-14}=\frac{-6}{-28}
=3/14
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-14}=\frac{0}{-28}
=0
$