(z^2-1)/5=7

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

(z^2-1)/5=7

We move all terms to the left:

(z^2-1)/5-(7)=0

We multiply all the terms by the denominator


(z^2-1)-7*5=0

We add all the numbers together, and all the variables

(z^2-1)-35=0

We get rid of parentheses

z^2-1-35=0

We add all the numbers together, and all the variables

z^2-36=0

a = 1; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·1·(-36)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*1}=\frac{-12}{2}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*1}=\frac{12}{2}
=6
$