(13/4)z=1/2

Solution for (13/4)z=1/2 equation:

(13/4)z=1/2

We move all terms to the left:

(13/4)z-(1/2)=0


Domain of the equation: 4)z!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

(+13/4)z-(+1/2)=0

We multiply parentheses

13z^2-(+1/2)=0

We get rid of parentheses

13z^2-1/2=0

We multiply all the terms by the denominator


13z^2*2-1=0

Wy multiply elements

26z^2-1=0

a = 26; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·26·(-1)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{26}}{2*26}=\frac{0-2\sqrt{26}}{52}
=-\frac{2\sqrt{26}}{52}
=-\frac{\sqrt{26}}{26}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{26}}{2*26}=\frac{0+2\sqrt{26}}{52}
=\frac{2\sqrt{26}}{52}
=\frac{\sqrt{26}}{26}
$