3/z+7/2z=2

Solution for 3/z+7/2z=2 equation:

3/z+7/2z=2

We move all terms to the left:

3/z+7/2z-(2)=0


Domain of the equation: z!=0

z∈R



Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We calculate fractions


6z/2z^2+7z/2z^2-2=0

We multiply all the terms by the denominator


6z+7z-2*2z^2=0

We add all the numbers together, and all the variables

13z-2*2z^2=0

Wy multiply elements

-4z^2+13z=0

a = -4; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-4)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-4}=\frac{-26}{-8}
=3+1/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-4}=\frac{0}{-8}
=0
$