(z+8)(6z-1)=0

Solution for (z+8)(6z-1)=0 equation:

(z+8)(6z-1)=0

We multiply parentheses ..

(+6z^2-1z+48z-8)=0

We get rid of parentheses

6z^2-1z+48z-8=0

We add all the numbers together, and all the variables

6z^2+47z-8=0

a = 6; b = 47; c = -8;
Δ = b2-4ac
Δ = 472-4·6·(-8)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-49}{2*6}=\frac{-96}{12}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+49}{2*6}=\frac{2}{12}
=1/6
$