5/z-1/5z=-3/10

Solution for 5/z-1/5z=-3/10 equation:

5/z-1/5z=-3/10

We move all terms to the left:

5/z-1/5z-(-3/10)=0


Domain of the equation: z!=0

z∈R



Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R


We get rid of parentheses

5/z-1/5z+3/10=0

We calculate fractions


75z^2/50z^2+250z/50z^2+(-10z)/50z^2=0

We multiply all the terms by the denominator


75z^2+250z+(-10z)=0

We get rid of parentheses

75z^2+250z-10z=0

We add all the numbers together, and all the variables

75z^2+240z=0

a = 75; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·75·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*75}=\frac{-480}{150}
=-3+1/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*75}=\frac{0}{150}
=0
$