1/763n-77=-11+9n

Solution for 1/763n-77=-11+9n equation:

1/763n-77=-11+9n

We move all terms to the left:

1/763n-77-(-11+9n)=0


Domain of the equation: 763n!=0

n!=0/763

n!=0

n∈R


We add all the numbers together, and all the variables

1/763n-(9n-11)-77=0

We get rid of parentheses

1/763n-9n+11-77=0

We multiply all the terms by the denominator


-9n*763n+11*763n-77*763n+1=0

Wy multiply elements

-6867n^2+8393n-58751n+1=0

We add all the numbers together, and all the variables

-6867n^2-50358n+1=0

a = -6867; b = -50358; c = +1;
Δ = b2-4ac
Δ = -503582-4·(-6867)·1
Δ = 2535955632
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:

$\sqrt{\Delta}=\sqrt{2535955632}=\sqrt{144*17610803}=\sqrt{144}*\sqrt{17610803}=12\sqrt{17610803}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50358)-12\sqrt{17610803}}{2*-6867}=\frac{50358-12\sqrt{17610803}}{-13734}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50358)+12\sqrt{17610803}}{2*-6867}=\frac{50358+12\sqrt{17610803}}{-13734}
$