1/13*j=19

Solution for 1/13*j=19 equation:

1/13*j=19

We move all terms to the left:

1/13*j-(19)=0


Domain of the equation: 13*j!=0

j!=0/1

j!=0

j∈R


We multiply all the terms by the denominator


-19*13*j+1=0

Wy multiply elements

-247j*j+1=0

Wy multiply elements

-247j^2+1=0

a = -247; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-247)·1
Δ = 988
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{247}}{2*-247}=\frac{0-2\sqrt{247}}{-494}
=-\frac{2\sqrt{247}}{-494}
=-\frac{\sqrt{247}}{-247}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{247}}{2*-247}=\frac{0+2\sqrt{247}}{-494}
=\frac{2\sqrt{247}}{-494}
=\frac{\sqrt{247}}{-247}
$