5n(2n)4(-3)=6(-3)(-1n)

Solution for 5n(2n)4(-3)=6(-3)(-1n) equation:

5n(2n)4(-3)=6(-3)(-1n)

We move all terms to the left:

5n(2n)4(-3)-(6(-3)(-1n))=0

We multiply parentheses

-15n^2-(6(-3)(-1n))=0

We multiply parentheses ..

-15n^2-(6(+3n))=0


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

6(+3n)

We multiply parentheses

18n

Back to the equation:

-(18n)


a = -15; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-15)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-15}=\frac{0}{-30}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-15}=\frac{36}{-30}
=-1+1/5
$