7/8z-4=-15/16z+1

Solution for 7/8z-4=-15/16z+1 equation:

7/8z-4=-15/16z+1

We move all terms to the left:

7/8z-4-(-15/16z+1)=0


Domain of the equation: 8z!=0

z!=0/8

z!=0

z∈R



Domain of the equation: 16z+1)!=0

z∈R


We get rid of parentheses

7/8z+15/16z-1-4=0

We calculate fractions


112z/128z^2+120z/128z^2-1-4=0

We add all the numbers together, and all the variables

112z/128z^2+120z/128z^2-5=0

We multiply all the terms by the denominator


112z+120z-5*128z^2=0

We add all the numbers together, and all the variables

232z-5*128z^2=0

Wy multiply elements

-640z^2+232z=0

a = -640; b = 232; c = 0;
Δ = b2-4ac
Δ = 2322-4·(-640)·0
Δ = 53824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{53824}=232$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(232)-232}{2*-640}=\frac{-464}{-1280}
=29/80
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(232)+232}{2*-640}=\frac{0}{-1280}
=0
$