1. **Problem Statement:** Find the value of $x$ that satisfies the equation $$8x^2 - 6x^3 = \frac{7}{3} - l$$ where $l$ is a constant. 2. **Rewrite the equation:** We want to isolate $x$. The equation is: $$8x^2 - 6x^3 = \frac{7}{3} - l$$ 3. **Rearrange terms:** Bring all terms to one side: $$8x^2 - 6x^3 - \frac{7}{3} + l = 0$$ 4. **Express as a polynomial in $x$:** $$-6x^3 + 8x^2 + (l - \frac{7}{3}) = 0$$ 5. **Solve for $x$:** This is a cubic equation in $x$. The general form is: $$ax^3 + bx^2 + cx + d = 0$$ Here, $a = -6$, $b = 8$, $c = 0$, and $d = l - \frac{7}{3}$. 6. **Use the cubic formula or numerical methods:** Since $c=0$, the equation simplifies to: $$-6x^3 + 8x^2 + (l - \frac{7}{3}) = 0$$ 7. **If $l$ is known, substitute and solve for $x$.** **Note:** Without a specific value for $l$, the exact numeric value of $x$ cannot be determined. **Summary:** The value(s) of $x$ satisfy the cubic equation: $$-6x^3 + 8x^2 + \left(l - \frac{7}{3}\right) = 0$$ You can solve this cubic equation for $x$ using standard methods once $l$ is known.