z^2=4/25

Solution for z^2=4/25 equation:

z^2=4/25

We move all terms to the left:

z^2-(4/25)=0

We add all the numbers together, and all the variables

z^2-(+4/25)=0

We get rid of parentheses

z^2-4/25=0

We multiply all the terms by the denominator


z^2*25-4=0

Wy multiply elements

25z^2-4=0

a = 25; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·25·(-4)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*25}=\frac{-20}{50}
=-2/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*25}=\frac{20}{50}
=2/5
$