(5/12)(n)=7/12

Solution for (5/12)(n)=7/12 equation:

(5/12)(n)=7/12

We move all terms to the left:

(5/12)(n)-(7/12)=0


Domain of the equation: 12)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+5/12)n-(+7/12)=0

We multiply parentheses

5n^2-(+7/12)=0

We get rid of parentheses

5n^2-7/12=0

We multiply all the terms by the denominator


5n^2*12-7=0

Wy multiply elements

60n^2-7=0

a = 60; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·60·(-7)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*60}=\frac{0-4\sqrt{105}}{120}
=-\frac{4\sqrt{105}}{120}
=-\frac{\sqrt{105}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*60}=\frac{0+4\sqrt{105}}{120}
=\frac{4\sqrt{105}}{120}
=\frac{\sqrt{105}}{30}
$