(-2x+4)(2x-5)=0

Solution for (-2x+4)(2x-5)=0 equation:

(-2x+4)(2x-5)=0

We multiply parentheses ..

(-4x^2+10x+8x-20)=0

We get rid of parentheses

-4x^2+10x+8x-20=0

We add all the numbers together, and all the variables

-4x^2+18x-20=0

a = -4; b = 18; c = -20;
Δ = b2-4ac
Δ = 182-4·(-4)·(-20)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2}{2*-4}=\frac{-20}{-8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2}{2*-4}=\frac{-16}{-8}
=+2
$