(5z-1)(5+z)=20

Solution for (5z-1)(5+z)=20 equation:

(5z-1)(5+z)=20

We move all terms to the left:

(5z-1)(5+z)-(20)=0

We add all the numbers together, and all the variables

(5z-1)(z+5)-20=0

We multiply parentheses ..

(+5z^2+25z-1z-5)-20=0

We get rid of parentheses

5z^2+25z-1z-5-20=0

We add all the numbers together, and all the variables

5z^2+24z-25=0

a = 5; b = 24; c = -25;
Δ = b2-4ac
Δ = 242-4·5·(-25)
Δ = 1076
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:

$\sqrt{\Delta}=\sqrt{1076}=\sqrt{4*269}=\sqrt{4}*\sqrt{269}=2\sqrt{269}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{269}}{2*5}=\frac{-24-2\sqrt{269}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{269}}{2*5}=\frac{-24+2\sqrt{269}}{10}
$