25z^2+98=100

Solution for 25z^2+98=100 equation:

25z^2+98=100

We move all terms to the left:

25z^2+98-(100)=0

We add all the numbers together, and all the variables

25z^2-2=0

a = 25; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·25·(-2)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*25}=\frac{0-10\sqrt{2}}{50}
=-\frac{10\sqrt{2}}{50}
=-\frac{\sqrt{2}}{5}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*25}=\frac{0+10\sqrt{2}}{50}
=\frac{10\sqrt{2}}{50}
=\frac{\sqrt{2}}{5}
$