(3z-8)(7+z)=0

Solution for (3z-8)(7+z)=0 equation:

(3z-8)(7+z)=0

We add all the numbers together, and all the variables

(3z-8)(z+7)=0

We multiply parentheses ..

(+3z^2+21z-8z-56)=0

We get rid of parentheses

3z^2+21z-8z-56=0

We add all the numbers together, and all the variables

3z^2+13z-56=0

a = 3; b = 13; c = -56;
Δ = b2-4ac
Δ = 132-4·3·(-56)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-29}{2*3}=\frac{-42}{6}
=-7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+29}{2*3}=\frac{16}{6}
=2+2/3
$