2z^2-8z+3=-z^2+2z

Solution for 2z^2-8z+3=-z^2+2z equation:

2z^2-8z+3=-z^2+2z

We move all terms to the left:

2z^2-8z+3-(-z^2+2z)=0

We get rid of parentheses

2z^2+z^2-2z-8z+3=0

We add all the numbers together, and all the variables

3z^2-10z+3=0

a = 3; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·3·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8}{2*3}=\frac{2}{6}
=1/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8}{2*3}=\frac{18}{6}
=3
$