(2x^2-3x+4)-(x^2-3x+13)=0

Solution for (2x^2-3x+4)-(x^2-3x+13)=0 equation:

Simplifying
(2x2 + -3x + 4) + -1(x2 + -3x + 13) = 0

Reorder the terms:
(4 + -3x + 2x2) + -1(x2 + -3x + 13) = 0

Remove parenthesis around (4 + -3x + 2x2)
4 + -3x + 2x2 + -1(x2 + -3x + 13) = 0

Reorder the terms:
4 + -3x + 2x2 + -1(13 + -3x + x2) = 0
4 + -3x + 2x2 + (13 * -1 + -3x * -1 + x2 * -1) = 0
4 + -3x + 2x2 + (-13 + 3x + -1x2) = 0

Reorder the terms:
4 + -13 + -3x + 3x + 2x2 + -1x2 = 0

Combine like terms: 4 + -13 = -9
-9 + -3x + 3x + 2x2 + -1x2 = 0

Combine like terms: -3x + 3x = 0
-9 + 0 + 2x2 + -1x2 = 0
-9 + 2x2 + -1x2 = 0

Combine like terms: 2x2 + -1x2 = 1x2
-9 + 1x2 = 0

Solving
-9 + 1x2 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + 1x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 1x2 = 0 + 9
1x2 = 0 + 9

Combine like terms: 0 + 9 = 9
1x2 = 9

Divide each side by '1'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}