(2z+7)(5-z)=0

Solution for (2z+7)(5-z)=0 equation:

(2z+7)(5-z)=0

We add all the numbers together, and all the variables

(2z+7)(-1z+5)=0

We multiply parentheses ..

(-2z^2+10z-7z+35)=0

We get rid of parentheses

-2z^2+10z-7z+35=0

We add all the numbers together, and all the variables

-2z^2+3z+35=0

a = -2; b = 3; c = +35;
Δ = b2-4ac
Δ = 32-4·(-2)·35
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{-(3)-17}{2*-2}=\frac{-20}{-4}
=+5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+17}{2*-2}=\frac{14}{-4}
=-3+1/2
$