5z^2-125=100

Solution for 5z^2-125=100 equation:

5z^2-125=100

We move all terms to the left:

5z^2-125-(100)=0

We add all the numbers together, and all the variables

5z^2-225=0

a = 5; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·5·(-225)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{5}}{2*5}=\frac{0-30\sqrt{5}}{10}
=-\frac{30\sqrt{5}}{10}
=-3\sqrt{5}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{5}}{2*5}=\frac{0+30\sqrt{5}}{10}
=\frac{30\sqrt{5}}{10}
=3\sqrt{5}
$