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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+5z^2+35z+2z+14)=0

We get rid of parentheses

5z^2+35z+2z+14=0

We add all the numbers together, and all the variables

5z^2+37z+14=0

a = 5; b = 37; c = +14;
Δ = b2-4ac
Δ = 372-4·5·14
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-33}{2*5}=\frac{-70}{10}
=-7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+33}{2*5}=\frac{-4}{10}
=-2/5
$