-10n=3/5n-8

Solution for -10n=3/5n-8 equation:

-10n=3/5n-8

We move all terms to the left:

-10n-(3/5n-8)=0


Domain of the equation: 5n-8)!=0

n∈R


We get rid of parentheses

-10n-3/5n+8=0

We multiply all the terms by the denominator


-10n*5n+8*5n-3=0

Wy multiply elements

-50n^2+40n-3=0

a = -50; b = 40; c = -3;
Δ = b2-4ac
Δ = 402-4·(-50)·(-3)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{10}}{2*-50}=\frac{-40-10\sqrt{10}}{-100}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{10}}{2*-50}=\frac{-40+10\sqrt{10}}{-100}
$