2/z-5=z/0.5*0.5z-7

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

2/z-5=z/0.5*0.5z-7

We move all terms to the left:

2/z-5-(z/0.5*0.5z-7)=0


Domain of the equation: z!=0

z∈R



Domain of the equation: 0.5*0.5z-7)!=0

z∈R


We get rid of parentheses

2/z-z/0.5*0.5z+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+2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

z^2+z=0

a = 1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·1·0
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*1}=\frac{-2}{2}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*1}=\frac{0}{2}
=0
$