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

We add all the numbers together, and all the variables

z^2-10z+3=0

a = 1; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·1·3
Δ = 88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{22}}{2*1}=\frac{10-2\sqrt{22}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{22}}{2*1}=\frac{10+2\sqrt{22}}{2}
$