1/2j+2=-13-3/4j

Solution for 1/2j+2=-13-3/4j equation:

1/2j+2=-13-3/4j

We move all terms to the left:

1/2j+2-(-13-3/4j)=0


Domain of the equation: 2j!=0

j!=0/2

j!=0

j∈R



Domain of the equation: 4j)!=0

j!=0/1

j!=0

j∈R


We add all the numbers together, and all the variables

1/2j-(-3/4j-13)+2=0

We get rid of parentheses

1/2j+3/4j+13+2=0

We calculate fractions


4j/8j^2+6j/8j^2+13+2=0

We add all the numbers together, and all the variables

4j/8j^2+6j/8j^2+15=0

We multiply all the terms by the denominator


4j+6j+15*8j^2=0

We add all the numbers together, and all the variables

10j+15*8j^2=0

Wy multiply elements

120j^2+10j=0

a = 120; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·120·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*120}=\frac{-20}{240}
=-1/12
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*120}=\frac{0}{240}
=0
$