1/9*i=13

Solution for 1/9*i=13 equation:

1/9*i=13

We move all terms to the left:

1/9*i-(13)=0


Domain of the equation: 9*i!=0

i!=0/1

i!=0

i∈R


We multiply all the terms by the denominator


-13*9*i+1=0

Wy multiply elements

-117i*i+1=0

Wy multiply elements

-117i^2+1=0

a = -117; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-117)·1
Δ = 468
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{13}}{2*-117}=\frac{0-6\sqrt{13}}{-234}
=-\frac{6\sqrt{13}}{-234}
=-\frac{\sqrt{13}}{-39}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{13}}{2*-117}=\frac{0+6\sqrt{13}}{-234}
=\frac{6\sqrt{13}}{-234}
=\frac{\sqrt{13}}{-39}
$