50/3n=7n+80

Solution for 50/3n=7n+80 equation:

50/3n=7n+80

We move all terms to the left:

50/3n-(7n+80)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

50/3n-7n-80=0

We multiply all the terms by the denominator


-7n*3n-80*3n+50=0

Wy multiply elements

-21n^2-240n+50=0

a = -21; b = -240; c = +50;
Δ = b2-4ac
Δ = -2402-4·(-21)·50
Δ = 61800
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:

$\sqrt{\Delta}=\sqrt{61800}=\sqrt{100*618}=\sqrt{100}*\sqrt{618}=10\sqrt{618}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-10\sqrt{618}}{2*-21}=\frac{240-10\sqrt{618}}{-42}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+10\sqrt{618}}{2*-21}=\frac{240+10\sqrt{618}}{-42}
$