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

Solution for (4+z)(5z-6)=0 equation:

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

We add all the numbers together, and all the variables

(z+4)(5z-6)=0

We multiply parentheses ..

(+5z^2-6z+20z-24)=0

We get rid of parentheses

5z^2-6z+20z-24=0

We add all the numbers together, and all the variables

5z^2+14z-24=0

a = 5; b = 14; c = -24;
Δ = b2-4ac
Δ = 142-4·5·(-24)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*5}=\frac{-40}{10}
=-4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*5}=\frac{12}{10}
=1+1/5
$