2z+24=2/7z

Solution for 2z+24=2/7z equation:

2z+24=2/7z

We move all terms to the left:

2z+24-(2/7z)=0


Domain of the equation: 7z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

2z-(+2/7z)+24=0

We get rid of parentheses

2z-2/7z+24=0

We multiply all the terms by the denominator


2z*7z+24*7z-2=0

Wy multiply elements

14z^2+168z-2=0

a = 14; b = 168; c = -2;
Δ = b2-4ac
Δ = 1682-4·14·(-2)
Δ = 28336
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:

$\sqrt{\Delta}=\sqrt{28336}=\sqrt{16*1771}=\sqrt{16}*\sqrt{1771}=4\sqrt{1771}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-4\sqrt{1771}}{2*14}=\frac{-168-4\sqrt{1771}}{28}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+4\sqrt{1771}}{2*14}=\frac{-168+4\sqrt{1771}}{28}
$