1/2n+7=n+142

Solution for 1/2n+7=n+142 equation:

1/2n+7=n+142

We move all terms to the left:

1/2n+7-(n+142)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

1/2n-n-142+7=0

We multiply all the terms by the denominator


-n*2n-142*2n+7*2n+1=0

Wy multiply elements

-2n^2-284n+14n+1=0

We add all the numbers together, and all the variables

-2n^2-270n+1=0

a = -2; b = -270; c = +1;
Δ = b2-4ac
Δ = -2702-4·(-2)·1
Δ = 72908
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:

$\sqrt{\Delta}=\sqrt{72908}=\sqrt{4*18227}=\sqrt{4}*\sqrt{18227}=2\sqrt{18227}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18227}}{2*-2}=\frac{270-2\sqrt{18227}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18227}}{2*-2}=\frac{270+2\sqrt{18227}}{-4}
$