5(4z)-(1/2)z=234

Solution for 5(4z)-(1/2)z=234 equation:

5(4z)-(1/2)z=234

We move all terms to the left:

5(4z)-(1/2)z-(234)=0


Domain of the equation: 2)z!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

54z-(+1/2)z-234=0

We multiply parentheses

-z^2+54z-234=0

We add all the numbers together, and all the variables

-1z^2+54z-234=0

a = -1; b = 54; c = -234;
Δ = b2-4ac
Δ = 542-4·(-1)·(-234)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{55}}{2*-1}=\frac{-54-6\sqrt{55}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{55}}{2*-1}=\frac{-54+6\sqrt{55}}{-2}
$