合并所有同类项，移到等号一边。 写下二次公式 ：{-b +/-√ (b2  - 4ac)}/2a  找出a、b、c的值。 把已知的a、b、c代入公式，按以下步骤来做：  算出解。 简化根式。 把正数解和负数解解出来。 解出两根：  简化解。

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Move all of the terms to one side of the equal sign, keeping the x2{\displaystyle x^{2}} term positive. Write the terms in descending order of degrees, so that the x2{\displaystyle x^{2}} term comes first, followed by the x{\displaystyle x} term and the constant term. Here's how you do it:  4x2 - 5x - 13 =  x2 -5 4x2 - x2 - 5x - 13 +5 = 0 3x2 - 5x - 8 = 0 The quadratic formula is: −b±b2−4ac2a{\displaystyle {\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}} The variable a is the coefficient of the x2 term, b is the coefficient of the x term, and c is the constant. For the equation 3x2 -5x - 8 = 0, a = 3, b = -5, and c = -8. Write this down. Now that you know the values of the three variables, you can just plug them into the equation like this:  {-b +/-√ (b2 - 4ac)}/2 {-(-5) +/-√ ((-5)2 - 4(3)(-8))}/2(3) = {-(-5) +/-√ ((-5)2 - (-96))}/2(3) After you've plugged in the numbers, do the remaining math to simplify positive or negative signs, multiply, or square the remaining terms. Here's how you do it:  {-(-5) +/-√ ((-5)2 - (-96))}/2(3) = {5 +/-√(25 + 96)}/6 {5 +/-√(121)}/6 If the number under the radical symbol is a perfect square, you will get a whole number. If the number is not a perfect square, then simplify to its simplest radical version. If the number is negative, and you're sure it's supposed to be negative, then the roots will be complex. In this example, √(121) = 11. You can write that x =  (5 +/- 11)/6. If you've eliminated the square root symbol, then you can keep going until you've found the positive and negative results for x. Now that you have (5 +/- 11)/6, you can write two options:  (5 + 11)/6 (5 - 11)/6 Just do the math:  (5 + 11)/6 = 16/6 (5-11)/6 = -6/6 To simplify each answer, just divide them by the largest number that is evenly divisible into both numbers. Divide the first fraction by 2, and divide the second by 6, and you have solved for x.  16/6 = 8/3 -6/6 = -1 x = (-1, 8/3)