-6n^-1=3-3n-7n^2

Solution for -6n^-1=3-3n-7n^2 equation:

-6n^-1=3-3n-7n^2

We move all terms to the left:

-6n^-1-(3-3n-7n^2)=0

We add all the numbers together, and all the variables

-(3-3n-7n^2)-6n-1=0

We get rid of parentheses

7n^2+3n-6n-3-1=0

We add all the numbers together, and all the variables

7n^2-3n-4=0

a = 7; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·7·(-4)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11}{2*7}=\frac{-8}{14}
=-4/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*7}=\frac{14}{14}
=1
$