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

Solution for (3+z)(5z-7)=0 equation:

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

We add all the numbers together, and all the variables

(z+3)(5z-7)=0

We multiply parentheses ..

(+5z^2-7z+15z-21)=0

We get rid of parentheses

5z^2-7z+15z-21=0

We add all the numbers together, and all the variables

5z^2+8z-21=0

a = 5; b = 8; c = -21;
Δ = b2-4ac
Δ = 82-4·5·(-21)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-22}{2*5}=\frac{-30}{10}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+22}{2*5}=\frac{14}{10}
=1+2/5
$