(4y-1)(2-y)=0

Solution for (4y-1)(2-y)=0 equation:

(4y-1)(2-y)=0

We add all the numbers together, and all the variables

(4y-1)(-1y+2)=0

We multiply parentheses ..

(-4y^2+8y+y-2)=0

We get rid of parentheses

-4y^2+8y+y-2=0

We add all the numbers together, and all the variables

-4y^2+9y-2=0

a = -4; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·(-4)·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*-4}=\frac{-16}{-8}
=+2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*-4}=\frac{-2}{-8}
=1/4
$