7/5n-6n=3

Solution for 7/5n-6n=3 equation:

7/5n-6n=3

We move all terms to the left:

7/5n-6n-(3)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

-6n+7/5n-3=0

We multiply all the terms by the denominator


-6n*5n-3*5n+7=0

Wy multiply elements

-30n^2-15n+7=0

a = -30; b = -15; c = +7;
Δ = b2-4ac
Δ = -152-4·(-30)·7
Δ = 1065
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{-(-15)-\sqrt{1065}}{2*-30}=\frac{15-\sqrt{1065}}{-60}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1065}}{2*-30}=\frac{15+\sqrt{1065}}{-60}
$