Question

Find the real solutions, if any, of the equation $3x^2+1=4x$.

Short answer

The solutions of the equation are$x=\left\{\frac{1}{3},1\right\}$.

Step-by-step solution

Step 1. Given Information

The given equation is$3x^2+1=4x$.

Step 2. Factor the Equation

• Write the equation in standard form.

$3x^2-4x+1=0$

• Factor the equations.

$\begin{array}{rcl}3x^2-3x-x+1& =& 0\\ (3x-1)(x-1)& =& 0\end{array}$

Step 3. Find the Solution

• Equate both the factors to 0 to find the solution.

$\begin{array}{rcl}3x-1& =& 0\\ x& =& \frac{1}{3}\\ x-1& =& 0\\ x& =& 1\end{array}$

• So, the solution set of$x$isrole="math" localid="1646704327562" $\left\{\frac{1}{3},1\right\}$.