3/7z-1/5z=8

Solution for 3/7z-1/5z=8 equation:

3/7z-1/5z=8

We move all terms to the left:

3/7z-1/5z-(8)=0


Domain of the equation: 7z!=0

z!=0/7

z!=0

z∈R



Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R


We calculate fractions


15z/35z^2+(-7z)/35z^2-8=0

We multiply all the terms by the denominator


15z+(-7z)-8*35z^2=0

Wy multiply elements

-280z^2+15z+(-7z)=0

We get rid of parentheses

-280z^2+15z-7z=0

We add all the numbers together, and all the variables

-280z^2+8z=0

a = -280; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-280)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-280}=\frac{-16}{-560}
=1/35
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-280}=\frac{0}{-560}
=0
$