5z^2=20z+25

Solution for 5z^2=20z+25 equation:

5z^2=20z+25

We move all terms to the left:

5z^2-(20z+25)=0

We get rid of parentheses

5z^2-20z-25=0

a = 5; b = -20; c = -25;
Δ = b2-4ac
Δ = -202-4·5·(-25)
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{-(-20)-30}{2*5}=\frac{-10}{10}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+30}{2*5}=\frac{50}{10}
=5
$