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

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

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

We move all terms to the left:

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


Domain of the equation: 2j+2))!=0

j∈R


We multiply all the terms by the denominator


4j*2j-2*2j+2))-(3(1+2))=0

We add all the numbers together, and all the variables

4j*2j-2*2j+2))-(33)=0

We add all the numbers together, and all the variables

4j*2j-2*2j=0

Wy multiply elements

8j^2-4j=0

a = 8; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·8·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*8}=\frac{0}{16}
=0
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*8}=\frac{8}{16}
=1/2
$