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^2-9z+2=0

a = 10; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·10·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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