Solve the equation $$ 20 x^{2}-7 x-6=0 $$ Answer: $$ x=\square $$

Question

UpStudy AI · Accepted Answer

To solve the quadratic equation $$ 20x^{2} - 7x - 6 = 0 $$, we can use the quadratic formula:

$$
x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
$$

Here, $$ a = 20 $$, $$ b = -7 $$, and $$ c = -6 $$.

1. **Calculate the discriminant ($$ \Delta $$):**

$$
\Delta = b^{2} - 4ac = (-7)^{2} - 4(20)(-6) = 49 + 480 = 529
$$

2. **Take the square root of the discriminant:**

$$
\sqrt{\Delta} = \sqrt{529} = 23
$$

3. **Apply the quadratic formula:**

$$
x = \frac{-(-7) \pm 23}{2 \times 20} = \frac{7 \pm 23}{40}
$$

This gives two possible solutions:

$$
x = \frac{7 + 23}{40} = \frac{30}{40} = \frac{3}{4}
$$

$$
x = \frac{7 - 23}{40} = \frac{-16}{40} = -\frac{2}{5}
$$

**Answer:**

$$
x = \frac{3}{4},\ -\frac{2}{5}
$$
The solutions are $$ x = \frac{3}{4} $$ and $$ x = -\frac{2}{5} $$.

Solve the equation \( 20 x^{2}-7 x-6=0 \) Answer: \( x=\square \)