(5+z)(5z-6)=0

Solution for (5+z)(5z-6)=0 equation:

(5+z)(5z-6)=0

We add all the numbers together, and all the variables

(z+5)(5z-6)=0

We multiply parentheses ..

(+5z^2-6z+25z-30)=0

We get rid of parentheses

5z^2-6z+25z-30=0

We add all the numbers together, and all the variables

5z^2+19z-30=0

a = 5; b = 19; c = -30;
Δ = b2-4ac
Δ = 192-4·5·(-30)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-31}{2*5}=\frac{-50}{10}
=-5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+31}{2*5}=\frac{12}{10}
=1+1/5
$