5z(2z-1)=-4z+2

Solution for 5z(2z-1)=-4z+2 equation:

5z(2z-1)=-4z+2

We move all terms to the left:

5z(2z-1)-(-4z+2)=0

We multiply parentheses

10z^2-5z-(-4z+2)=0

We get rid of parentheses

10z^2-5z+4z-2=0

We add all the numbers together, and all the variables

10z^2-1z-2=0

a = 10; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·10·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*10}=\frac{-8}{20}
=-2/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*10}=\frac{10}{20}
=1/2
$