(4n^2+2n-83)/(2n-9)=0

Solution for (4n^2+2n-83)/(2n-9)=0 equation:

(4n^2+2n-83)/(2n-9)=0


Domain of the equation: (2n-9)!=0

We move all terms containing n to the left, all other terms to the right

2n!=9

n!=9/2

n!=4+1/2

n∈R


We multiply all the terms by the denominator


(4n^2+2n-83)=0

We get rid of parentheses

4n^2+2n-83=0

a = 4; b = 2; c = -83;
Δ = b2-4ac
Δ = 22-4·4·(-83)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{37}}{2*4}=\frac{-2-6\sqrt{37}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{37}}{2*4}=\frac{-2+6\sqrt{37}}{8}
$