9/j-7j=72

Solution for 9/j-7j=72 equation:

9/j-7j=72

We move all terms to the left:

9/j-7j-(72)=0


Domain of the equation: j!=0

j∈R


We add all the numbers together, and all the variables

-7j+9/j-72=0

We multiply all the terms by the denominator


-7j*j-72*j+9=0

We add all the numbers together, and all the variables

-72j-7j*j+9=0

Wy multiply elements

-7j^2-72j+9=0

a = -7; b = -72; c = +9;
Δ = b2-4ac
Δ = -722-4·(-7)·9
Δ = 5436
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:

$\sqrt{\Delta}=\sqrt{5436}=\sqrt{36*151}=\sqrt{36}*\sqrt{151}=6\sqrt{151}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{151}}{2*-7}=\frac{72-6\sqrt{151}}{-14}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{151}}{2*-7}=\frac{72+6\sqrt{151}}{-14}
$