12х+7х2=-5
To solve the equation \( 12x + 7x^2 = -5 \), we first rearrange it into standard quadratic form:
\[ 7x^2 + 12x + 5 = 0 \]
Next, we can apply the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \( a = 7 \), \( b = 12 \), and \( c = 5 \).
First, we calculate the discriminant \( b^2 - 4ac \):
\[ b^2 = 12^2 = 144 \] \[ 4ac = 4 \times 7 \times 5 = 140 \] \[ b^2 - 4ac = 144 - 140 = 4 \]
Now, we can find the values of \( x \):
\[ x = \frac{-12 \pm \sqrt{4}}{2 \times 7} \]
\[ x = \frac{-12 \pm 2}{14} \]
This gives us two solutions:
\( x = \frac{-12 + 2}{14} = \frac{-10}{14} = -\frac{5}{7} \)
\( x = \frac{-12 - 2}{14} = \frac{-14}{14} = -1 \)
Thus, the solutions to the equation \( 12x + 7x^2 = -5 \) are:
\[ x = -\frac{5}{7} \quad \text{and} \quad x = -1 \]
