1/4n+6=2n-15

Solution for 1/4n+6=2n-15 equation:

1/4n+6=2n-15

We move all terms to the left:

1/4n+6-(2n-15)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We get rid of parentheses

1/4n-2n+15+6=0

We multiply all the terms by the denominator


-2n*4n+15*4n+6*4n+1=0

Wy multiply elements

-8n^2+60n+24n+1=0

We add all the numbers together, and all the variables

-8n^2+84n+1=0

a = -8; b = 84; c = +1;
Δ = b2-4ac
Δ = 842-4·(-8)·1
Δ = 7088
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:

$\sqrt{\Delta}=\sqrt{7088}=\sqrt{16*443}=\sqrt{16}*\sqrt{443}=4\sqrt{443}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{443}}{2*-8}=\frac{-84-4\sqrt{443}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{443}}{2*-8}=\frac{-84+4\sqrt{443}}{-16}
$