(2z+3)(7-z)=0

Solution for (2z+3)(7-z)=0 equation:

(2z+3)(7-z)=0

We add all the numbers together, and all the variables

(2z+3)(-1z+7)=0

We multiply parentheses ..

(-2z^2+14z-3z+21)=0

We get rid of parentheses

-2z^2+14z-3z+21=0

We add all the numbers together, and all the variables

-2z^2+11z+21=0

a = -2; b = 11; c = +21;
Δ = b2-4ac
Δ = 112-4·(-2)·21
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-17}{2*-2}=\frac{-28}{-4}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+17}{2*-2}=\frac{6}{-4}
=-1+1/2
$