May you please help me with this?

        4x² — 8x = 5

Get 0 on the right by adding -5 to both sides

    4x² — 8x — 5 = 0

Now we factor the left side


    4x² — 8x — 5 = 0

4x² — 8x — 5 = 0

Multiply the red 4 by the blue 5, which gives
20, Now since the green sign is " — ", we 
think of two integers which have product equal
to 20 and which have difference equal to the 
purple 8.

Such integers are 10 and 2. So we use these to
rewrite the -8x as -10x + 2x

4x² - 10x + 2x - 5 = 0

Now we factor 2x out of the first two terms

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

Now we factor 1 out of the last two terms:

2x(2x - 5) + 1(2x - 5) = 0

Notice there is a common factor of (2x - 5)

So take out the common
factor (2x - 5) and put the factors 2x and +1
inside parentheses on the right:

(2x - 5)(2x + 1) = 0

Now we set each factor in parentheses equal to
0 and solve

Setting 2x - 5 = 0
            2x = 5
             x = 5/2

Setting 2x + 1 = 0
            2x = -1
             x = -1/2 

So the two solutions are 5/2 and -1/2

Edwin