3/4z+4=-5/8z

Solution for 3/4z+4=-5/8z equation:

3/4z+4=-5/8z

We move all terms to the left:

3/4z+4-(-5/8z)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R



Domain of the equation: 8z)!=0

z!=0/1

z!=0

z∈R


We get rid of parentheses

3/4z+5/8z+4=0

We calculate fractions


24z/32z^2+20z/32z^2+4=0

We multiply all the terms by the denominator


24z+20z+4*32z^2=0

We add all the numbers together, and all the variables

44z+4*32z^2=0

Wy multiply elements

128z^2+44z=0

a = 128; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·128·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*128}=\frac{-88}{256}
=-11/32
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*128}=\frac{0}{256}
=0
$