7/8z-1=1/25z

Solution for 7/8z-1=1/25z equation:

7/8z-1=1/25z

We move all terms to the left:

7/8z-1-(1/25z)=0


Domain of the equation: 8z!=0

z!=0/8

z!=0

z∈R



Domain of the equation: 25z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

7/8z-(+1/25z)-1=0

We get rid of parentheses

7/8z-1/25z-1=0

We calculate fractions


175z/200z^2+(-8z)/200z^2-1=0

We multiply all the terms by the denominator


175z+(-8z)-1*200z^2=0

Wy multiply elements

-200z^2+175z+(-8z)=0

We get rid of parentheses

-200z^2+175z-8z=0

We add all the numbers together, and all the variables

-200z^2+167z=0

a = -200; b = 167; c = 0;
Δ = b2-4ac
Δ = 1672-4·(-200)·0
Δ = 27889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27889}=167$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(167)-167}{2*-200}=\frac{-334}{-400}
=167/200
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(167)+167}{2*-200}=\frac{0}{-400}
=0
$