62+j=74/j=12

Solution for 62+j=74/j=12 equation:

62+j=74/j=12

We move all terms to the left:

62+j-(74/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-(+74/j)+62=0

We get rid of parentheses

j-74/j+62=0

We multiply all the terms by the denominator


j*j+62*j-74=0

We add all the numbers together, and all the variables

62j+j*j-74=0

Wy multiply elements

j^2+62j-74=0

a = 1; b = 62; c = -74;
Δ = b2-4ac
Δ = 622-4·1·(-74)
Δ = 4140
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:

$\sqrt{\Delta}=\sqrt{4140}=\sqrt{36*115}=\sqrt{36}*\sqrt{115}=6\sqrt{115}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-6\sqrt{115}}{2*1}=\frac{-62-6\sqrt{115}}{2}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+6\sqrt{115}}{2*1}=\frac{-62+6\sqrt{115}}{2}
$