Solve the quadratic equation: $2x^2 - 7x + 3 = 0$

Step 1: Identify coefficients

We first identify the coefficients $a$, $b$, and $c$ from the given quadratic equation $2x^2 - 7x + 3 = 0$. These coefficients are essential for applying the quadratic formula.

Step 2: Apply the quadratic formula

The quadratic formula is used to find the roots of any quadratic equation in the form $ax^2 + bx + c = 0$. This formula provides a direct method to solve for $x$.

Step 3: Substitute values into the formula

Now we substitute the values of $a=2$, $b=-7$, and $c=3$ into the quadratic formula. Careful substitution helps prevent errors in calculation.

Step 4: Simplify the expression under the square root

We calculate the terms inside the square root. $(-7)^2$ becomes $49$, and $4(2)(3)$ becomes $24$. The denominator $2(2)$ becomes $4$.

Step 5: Calculate the square root

Subtracting $24$ from $49$ gives $25$. The square root of $25$ is $5$. We now have a simplified expression ready for finding the two possible values of $x$.

Step 6: Calculate the two possible values for x

The $\pm$ sign indicates two solutions. We calculate one root using the positive sign and the other root using the negative sign.

Step 7: Final calculation of roots

Performing the final division, we find the two roots of the quadratic equation. The first root is $3$ and the second root is $1/2$.

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