13/18*n=91

Solution for 13/18*n=91 equation:

13/18*n=91

We move all terms to the left:

13/18*n-(91)=0


Domain of the equation: 18*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-91*18*n+13=0

Wy multiply elements

-1638n*n+13=0

Wy multiply elements

-1638n^2+13=0

a = -1638; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-1638)·13
Δ = 85176
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:

$\sqrt{\Delta}=\sqrt{85176}=\sqrt{6084*14}=\sqrt{6084}*\sqrt{14}=78\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-78\sqrt{14}}{2*-1638}=\frac{0-78\sqrt{14}}{-3276}
=-\frac{78\sqrt{14}}{-3276}
=-\frac{\sqrt{14}}{-42}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+78\sqrt{14}}{2*-1638}=\frac{0+78\sqrt{14}}{-3276}
=\frac{78\sqrt{14}}{-3276}
=\frac{\sqrt{14}}{-42}
$