25z^2+97=100z

Solution for 25z^2+97=100z equation:

25z^2+97=100z

We move all terms to the left:

25z^2+97-(100z)=0

a = 25; b = -100; c = +97;
Δ = b2-4ac
Δ = -1002-4·25·97
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-10\sqrt{3}}{2*25}=\frac{100-10\sqrt{3}}{50}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+10\sqrt{3}}{2*25}=\frac{100+10\sqrt{3}}{50}
$