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

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

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

We add all the numbers together, and all the variables

(5z+6)(-1z+5)=0

We multiply parentheses ..

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

We get rid of parentheses

-5z^2+25z-6z+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
$