Solve $6x^2 + 5x - 6 = 0$ - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 2

Since this is a quadratic equation in the form $ax^2 + bx + c = 0$, we will apply the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Here, $a = 6$, $b = 5$, and $c = -6$.

Now, substituting the values into the formula:

1. Calculate the discriminant:
   $b^2 - 4ac = 5^2 - 4(6)(-6) = 25 + 144 = 169$
2. Now applying the values into the quadratic formula:
   $x = \frac{-5 \pm \sqrt{169}}{2(6)} = \frac{-5 \pm 13}{12}$
3. This gives two solutions:
   • For $x = \frac{-5 + 13}{12} = \frac{8}{12} = \frac{2}{3}$
   • For $x = \frac{-5 - 13}{12} = \frac{-18}{12} = -\frac{3}{2}$
     Thus, the solutions are:
     $x = \frac{2}{3}, -\frac{3}{2}$