30/n-7n+12=-7-18

Solution for 30/n-7n+12=-7-18 equation:

30/n-7n+12=-7-18

We move all terms to the left:

30/n-7n+12-(-7-18)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

30/n-7n+12-(-25)=0

We add all the numbers together, and all the variables

-7n+30/n+37=0

We multiply all the terms by the denominator


-7n*n+37*n+30=0

We add all the numbers together, and all the variables

37n-7n*n+30=0

Wy multiply elements

-7n^2+37n+30=0

a = -7; b = 37; c = +30;
Δ = b2-4ac
Δ = 372-4·(-7)·30
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-47}{2*-7}=\frac{-84}{-14}
=+6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+47}{2*-7}=\frac{10}{-14}
=-5/7
$