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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+4z^2-6z+20z-30)=0

We get rid of parentheses

4z^2-6z+20z-30=0

We add all the numbers together, and all the variables

4z^2+14z-30=0

a = 4; b = 14; c = -30;
Δ = b2-4ac
Δ = 142-4·4·(-30)
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*4}=\frac{-40}{8}
=-5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*4}=\frac{12}{8}
=1+1/2
$