(2/3)z=41/4

Solution for (2/3)z=41/4 equation:

(2/3)z=41/4

We move all terms to the left:

(2/3)z-(41/4)=0


Domain of the equation: 3)z!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

(+2/3)z-(+41/4)=0

We multiply parentheses

2z^2-(+41/4)=0

We get rid of parentheses

2z^2-41/4=0

We multiply all the terms by the denominator


2z^2*4-41=0

Wy multiply elements

8z^2-41=0

a = 8; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·8·(-41)
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{82}}{2*8}=\frac{0-4\sqrt{82}}{16}
=-\frac{4\sqrt{82}}{16}
=-\frac{\sqrt{82}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{82}}{2*8}=\frac{0+4\sqrt{82}}{16}
=\frac{4\sqrt{82}}{16}
=\frac{\sqrt{82}}{4}
$