.5*j*10=400/j

Solution for .5*j*10=400/j equation:

.5j*10=400/j

We move all terms to the left:

.5j*10-(400/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

.5j*10-(+400/j)=0

We get rid of parentheses

.5j*10-400/j=0

We multiply all the terms by the denominator


(.5j*10)*j-400=0

We add all the numbers together, and all the variables

(+.5j*10)*j-400=0

We multiply parentheses

10j^2-400=0

a = 10; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·10·(-400)
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{10}}{2*10}=\frac{0-40\sqrt{10}}{20}
=-\frac{40\sqrt{10}}{20}
=-2\sqrt{10}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{10}}{2*10}=\frac{0+40\sqrt{10}}{20}
=\frac{40\sqrt{10}}{20}
=2\sqrt{10}
$