1. **State the problem:** Solve the quadratic equation $$6w^2 - 26w + 5 = w^2$$ for $w$ using the quadratic formula. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$6w^2 - 26w + 5 - w^2 = 0$$ Simplify: $$5w^2 - 26w + 5 = 0$$ 3. **Identify coefficients:** For the quadratic equation $$aw^2 + bw + c = 0$$, here: $$a = 5, \quad b = -26, \quad c = 5$$ 4. **Quadratic formula:** $$w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-26)^2 - 4 \times 5 \times 5 = 676 - 100 = 576$$ 6. **Square root of discriminant:** $$\sqrt{576} = 24$$ 7. **Apply the quadratic formula:** $$w = \frac{-(-26) \pm 24}{2 \times 5} = \frac{26 \pm 24}{10}$$ 8. **Find the two solutions:** - For the plus sign: $$w = \frac{26 + 24}{10} = \frac{50}{10} = 5$$ - For the minus sign: $$w = \frac{26 - 24}{10} = \frac{2}{10} = \frac{1}{5}$$ 9. **Final answer:** $$w = 5 \quad \text{or} \quad w = \frac{1}{5}$$