25z^2=50z+75

Solution for 25z^2=50z+75 equation:

25z^2=50z+75

We move all terms to the left:

25z^2-(50z+75)=0

We get rid of parentheses

25z^2-50z-75=0

a = 25; b = -50; c = -75;
Δ = b2-4ac
Δ = -502-4·25·(-75)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-100}{2*25}=\frac{-50}{50}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+100}{2*25}=\frac{150}{50}
=3
$