7/z+5=-3/5z

Solution for 7/z+5=-3/5z equation:

7/z+5=-3/5z

We move all terms to the left:

7/z+5-(-3/5z)=0


Domain of the equation: z!=0

z∈R



Domain of the equation: 5z)!=0

z!=0/1

z!=0

z∈R


We get rid of parentheses

7/z+3/5z+5=0

We calculate fractions


35z/5z^2+3z/5z^2+5=0

We multiply all the terms by the denominator


35z+3z+5*5z^2=0

We add all the numbers together, and all the variables

38z+5*5z^2=0

Wy multiply elements

25z^2+38z=0

a = 25; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·25·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*25}=\frac{-76}{50}
=-1+13/25
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*25}=\frac{0}{50}
=0
$