3/4z-2=z

Solution for 3/4z-2=z equation:

3/4z-2=z

We move all terms to the left:

3/4z-2-(z)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4z^2-8z+3=0

a = -4; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-4)·3
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*-4}=\frac{8-4\sqrt{7}}{-8}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*-4}=\frac{8+4\sqrt{7}}{-8}
$