3-1/2z=z

Solution for 3-1/2z=z equation:

3-1/2z=z

We move all terms to the left:

3-1/2z-(z)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-2z^2+6z-1=0

a = -2; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-2)·(-1)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{7}}{2*-2}=\frac{-6-2\sqrt{7}}{-4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{7}}{2*-2}=\frac{-6+2\sqrt{7}}{-4}
$