4/5n+7=n+14/2

Solution for 4/5n+7=n+14/2 equation:

4/5n+7=n+14/2

We move all terms to the left:

4/5n+7-(n+14/2)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

4/5n-(n+7)+7=0

We get rid of parentheses

4/5n-n-7+7=0

We multiply all the terms by the denominator


-n*5n-7*5n+7*5n+4=0

Wy multiply elements

-5n^2-35n+35n+4=0

We add all the numbers together, and all the variables

-5n^2+4=0

a = -5; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-5)·4
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*-5}=\frac{0-4\sqrt{5}}{-10}
=-\frac{4\sqrt{5}}{-10}
=-\frac{2\sqrt{5}}{-5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*-5}=\frac{0+4\sqrt{5}}{-10}
=\frac{4\sqrt{5}}{-10}
=\frac{2\sqrt{5}}{-5}
$