-z^2-2z+2=-3z+z^2-7

Solution for -z^2-2z+2=-3z+z^2-7 equation:

-z^2-2z+2=-3z+z^2-7

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-1z^2-z^2+3z-2z+7+2=0

We add all the numbers together, and all the variables

-2z^2+z+9=0

a = -2; b = 1; c = +9;
Δ = b2-4ac
Δ = 12-4·(-2)·9
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{73}}{2*-2}=\frac{-1-\sqrt{73}}{-4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{73}}{2*-2}=\frac{-1+\sqrt{73}}{-4}
$