(6+z)(2z-7)=0

Solution for (6+z)(2z-7)=0 equation:

(6+z)(2z-7)=0

We add all the numbers together, and all the variables

(z+6)(2z-7)=0

We multiply parentheses ..

(+2z^2-7z+12z-42)=0

We get rid of parentheses

2z^2-7z+12z-42=0

We add all the numbers together, and all the variables

2z^2+5z-42=0

a = 2; b = 5; c = -42;
Δ = b2-4ac
Δ = 52-4·2·(-42)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*2}=\frac{-24}{4}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*2}=\frac{14}{4}
=3+1/2
$