n-7/12n=25

Solution for n-7/12n=25 equation:

n-7/12n=25

We move all terms to the left:

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


Domain of the equation: 12n!=0

n!=0/12

n!=0

n∈R


We multiply all the terms by the denominator


n*12n-25*12n-7=0

Wy multiply elements

12n^2-300n-7=0

a = 12; b = -300; c = -7;
Δ = b2-4ac
Δ = -3002-4·12·(-7)
Δ = 90336
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:

$\sqrt{\Delta}=\sqrt{90336}=\sqrt{16*5646}=\sqrt{16}*\sqrt{5646}=4\sqrt{5646}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-4\sqrt{5646}}{2*12}=\frac{300-4\sqrt{5646}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+4\sqrt{5646}}{2*12}=\frac{300+4\sqrt{5646}}{24}
$