Find the roots of the equation 2x^2-3=5x using factors

We'll re-write the equation having all terms to the left
side:

2x^2 - 5x - 3 = 0

We'll
apply the quadratic formula:

x1 =
[5+sqrt(25+24)]/4

x1 =
(5+7)/4

x1 = 3

x2 =
(5-7)/4

x2 = -1/2

We'll write
the equation according as a product of linear factors:

2x^2
- 5x - 3 = 2(x - x1)(x - x2)

2x^2 - 5x - 3 =
2(x - 3)(x + 1/2)

We can also
re-write the term 5x from the right side as the sum :2x +
3x.

Now, we'll re-write the entire
equation:

2x^2-3 = 2x +
3x

We'll subtract 3x both sides and we'll add 3 both
sides:

2x^2 - 3 + 3 - 3x = 2x + 3x + 3 -
3x

We'll combine and eliminate like
terms:

2x^2 - 3x = 2x +
3

We'll factorize by x to the left
side:

x(2x - 3) = 2x + 3