67-j=25/j=42

Solution for 67-j=25/j=42 equation:

67-j=25/j=42

We move all terms to the left:

67-j-(25/j)=0


Domain of the equation: j)!=0

j!=0/1

j!=0

j∈R


We add all the numbers together, and all the variables

-j-(+25/j)+67=0

We add all the numbers together, and all the variables

-1j-(+25/j)+67=0

We get rid of parentheses

-1j-25/j+67=0

We multiply all the terms by the denominator


-1j*j+67*j-25=0

We add all the numbers together, and all the variables

67j-1j*j-25=0

Wy multiply elements

-1j^2+67j-25=0

a = -1; b = 67; c = -25;
Δ = b2-4ac
Δ = 672-4·(-1)·(-25)
Δ = 4389
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-\sqrt{4389}}{2*-1}=\frac{-67-\sqrt{4389}}{-2}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+\sqrt{4389}}{2*-1}=\frac{-67+\sqrt{4389}}{-2}
$