10x2 + 3x-7=0

To solve the quadratic equation \( 10x^2 + 3x - 7 = 0 \), we can use the quadratic formula:

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

In this case, the coefficients are:

• \( a = 10 \)
• \( b = 3 \)
• \( c = -7 \)

Now, we can calculate the discriminant \( b^2 - 4ac \):

\[ b^2 = 3^2 = 9 \] \[ 4ac = 4 \cdot 10 \cdot (-7) = -280 \] \[ b^2 - 4ac = 9 - (-280) = 9 + 280 = 289 \]

Now we can substitute the values into the quadratic formula:

\[ x = \frac{{-3 \pm \sqrt{289}}}{2 \cdot 10} \]

Calculating the square root:

\[ \sqrt{289} = 17 \]

Now, substituting back into the equation:

\[ x = \frac{{-3 \pm 17}}{20} \]

This gives us two potential solutions:

1. \( x = \frac{{-3 + 17}}{20} = \frac{14}{20} = \frac{7}{10} \)
2. \( x = \frac{{-3 - 17}}{20} = \frac{{-20}}{20} = -1 \)

Thus, the solutions to the equation \( 10x^2 + 3x - 7 = 0 \) are:

\[ x = \frac{7}{10} \quad \text{and} \quad x = -1 \]