2/z-5=z/0.5z^2+7

Solution for 2/z-5=z/0.5z^2+7 equation:

2/z-5=z/0.5z^2+7

We move all terms to the left:

2/z-5-(z/0.5z^2+7)=0


Domain of the equation: z!=0

z∈R



Domain of the equation: 0.5z^2+7)!=0

z∈R


We get rid of parentheses

2/z-z/0.5z^2-7-5=0

We calculate fractions


(-1z^2)/z^2+z/z^2-7-5=0

We add all the numbers together, and all the variables

(-1z^2)/z^2+z/z^2-12=0

We multiply all the terms by the denominator


(-1z^2)+z-12*z^2=0

We add all the numbers together, and all the variables

-12z^2+(-1z^2)+z=0

We get rid of parentheses

-12z^2-1z^2+z=0

We add all the numbers together, and all the variables

-13z^2+z=0

a = -13; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-13)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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