To rewrite the given quadratic equation \( 6x^2 = 22x \) in standard form, we need to move all terms to one side of the equation. Subtracting \( 22x \) from both sides gives:
\[ 6x^2 - 22x = 0 \]
Next, we can factor out the greatest common factor (GCF) from the left side of the equation. The GCF of \( 6x^2 \) and \( -22x \) is \( 2x \):
\[ 2x(3x - 11) = 0 \]
Now, we set each factor equal to zero.
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\( 2x = 0 \) \[ x = 0 \]
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\( 3x - 11 = 0 \) \[ 3x = 11 \quad \Rightarrow \quad x = \frac{11}{3} \]
Thus, we have the solutions:
- Smaller solution: \( x = 0 \)
- Larger solution: \( x = \frac{11}{3} \)
In summary, the smaller solution is \( x = 0 \), and the larger solution is \( x = \frac{11}{3} \).