2z^2=z^2+225

Solution for 2z^2=z^2+225 equation:

2z^2=z^2+225

We move all terms to the left:

2z^2-(z^2+225)=0

We get rid of parentheses

2z^2-z^2-225=0

We add all the numbers together, and all the variables

z^2-225=0

a = 1; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·1·(-225)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*1}=\frac{-30}{2}
=-15
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*1}=\frac{30}{2}
=15
$