0.7*x^2=1.3*x+2

To solve the equation \( 0.7x^2 = 1.3x + 2 \), we first rearrange it into standard quadratic form \( ax^2 + bx + c = 0 \).

Starting with:

\[ 0.7x^2 - 1.3x - 2 = 0 \]

Now, we can use the quadratic formula to find the solutions for \( x \):

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

Here, \( a = 0.7 \), \( b = -1.3 \), and \( c = -2 \).

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

\[ b^2 = (-1.3)^2 = 1.69 \] \[ 4ac = 4 \times 0.7 \times -2 = -5.6 \] \[ b^2 - 4ac = 1.69 - (-5.6) = 1.69 + 5.6 = 7.29 \]

Now substituting into the quadratic formula:

\[ x = \frac{-(-1.3) \pm \sqrt{7.29}}{2 \times 0.7} \] \[ x = \frac{1.3 \pm 2.7}{1.4} \]

This gives us two values for \( x \):

1. \( x = \frac{1.3 + 2.7}{1.4} = \frac{4}{1.4} = \frac{20}{7} \approx 2.857 \)
2. \( x = \frac{1.3 - 2.7}{1.4} = \frac{-1.4}{1.4} = -1 \)

Thus, the solutions to the equation \( 0.7x^2 = 1.3x + 2 \) are:

\[ x = \frac{20}{7} \quad \text{and} \quad x = -1 \]