3/5n+12=2n-9

Solution for 3/5n+12=2n-9 equation:

3/5n+12=2n-9

We move all terms to the left:

3/5n+12-(2n-9)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We get rid of parentheses

3/5n-2n+9+12=0

We multiply all the terms by the denominator


-2n*5n+9*5n+12*5n+3=0

Wy multiply elements

-10n^2+45n+60n+3=0

We add all the numbers together, and all the variables

-10n^2+105n+3=0

a = -10; b = 105; c = +3;
Δ = b2-4ac
Δ = 1052-4·(-10)·3
Δ = 11145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-\sqrt{11145}}{2*-10}=\frac{-105-\sqrt{11145}}{-20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11145}}{2*-10}=\frac{-105+\sqrt{11145}}{-20}
$