z*z-+3*(z+z-)=7

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

z*z-+3(z+z-)=7

We move all terms to the left:

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

determiningTheFunctionDomain
z*z+3(z+z-)-7-=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

z*z+3(+2z)=0

We multiply parentheses

z*z+6z=0

Wy multiply elements

z^2+6z=0

a = 1; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·1·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*1}=\frac{-12}{2}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*1}=\frac{0}{2}
=0
$