3/4*z=1/4*z-3+5

Solution for 3/4*z=1/4*z-3+5 equation:

3/4*z=1/4*z-3+5

We move all terms to the left:

3/4*z-(1/4*z-3+5)=0


Domain of the equation: 4*z!=0

z!=0/1

z!=0

z∈R



Domain of the equation: 4*z-3+5)!=0

We move all terms containing z to the left, all other terms to the right

4*z+5)!=3

z∈R


We add all the numbers together, and all the variables

3/4*z-(1/4*z+2)=0

We get rid of parentheses

3/4*z-1/4*z-2=0

We multiply all the terms by the denominator


-2*4*z+3-1=0

We add all the numbers together, and all the variables

-2*4*z+2=0

Wy multiply elements

-8z*z+2=0

Wy multiply elements

-8z^2+2=0

a = -8; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-8)·2
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{-(0)-8}{2*-8}=\frac{-8}{-16}
=1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-8}=\frac{8}{-16}
=-1/2
$