7/8z-2=15/16z+3

Solution for 7/8z-2=15/16z+3 equation:

7/8z-2=15/16z+3

We move all terms to the left:

7/8z-2-(15/16z+3)=0


Domain of the equation: 8z!=0

z!=0/8

z!=0

z∈R



Domain of the equation: 16z+3)!=0

z∈R


We get rid of parentheses

7/8z-15/16z-3-2=0

We calculate fractions


112z/128z^2+(-120z)/128z^2-3-2=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

Wy multiply elements

-640z^2+112z+(-120z)=0

We get rid of parentheses

-640z^2+112z-120z=0

We add all the numbers together, and all the variables

-640z^2-8z=0

a = -640; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-640)·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*-640}=\frac{0}{-1280}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-640}=\frac{16}{-1280}
=-1/80
$