Solve for x: $2x^2 - 7x + 3 = 0$. I am a class 10 student, please help me understand how to do it.

Step 1: Identify coefficients

The given equation is $2x^2 - 7x + 3 = 0$. This is a quadratic equation in the standard form $ax^2 + bx + c = 0$. By comparing the given equation with the standard form, we can identify the coefficients $a$, $b$, and $c$.

Step 2: Apply the quadratic formula

Now that we have the values of $a$, $b$, and $c$, we can use the quadratic formula to find the values of $x$. The quadratic formula provides the solutions for any quadratic equation.

Step 3: Substitute values into the formula

Substitute the identified values $a = 2$, $b = -7$, and $c = 3$ into the quadratic formula. Be careful with the signs, especially for the term $-b$.

Step 4: Simplify the expression

First, calculate the term inside the square root, which is the discriminant $b^2 - 4ac$. Then, simplify the square root and the denominator.

Step 5: Calculate the two possible values for x

The $\pm$ sign in the quadratic formula indicates that there are two possible solutions for $x$. Calculate each solution separately, one using the plus sign and the other using the minus sign.

Step 6: Final solutions

Perform the final division for both expressions to get the two solutions for $x$. These are the roots of the quadratic equation.

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