(1/4)z-2/7=5/7

Solution for (1/4)z-2/7=5/7 equation:

(1/4)z-2/7=5/7

We move all terms to the left:

(1/4)z-2/7-(5/7)=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

(+1/4)z-2/7-(+5/7)=0

We multiply parentheses

z^2-2/7-(+5/7)=0

We get rid of parentheses

z^2-2/7-5/7=0

We multiply all the terms by the denominator


z^2*7-2-5=0

We add all the numbers together, and all the variables

z^2*7-7=0

Wy multiply elements

7z^2-7=0

a = 7; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·7·(-7)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*7}=\frac{-14}{14}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*7}=\frac{14}{14}
=1
$