Problem

Solve for $x$. \[ 5 x^{2}-3=14 x \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

Solution

Step 1 :Rearrange the equation to the form of \(ax^2 + bx + c = 0\), which gives us \(5x^2 - 14x - 3 = 0\).

Step 2 :Identify the coefficients as \(a = 5\), \(b = -14\), and \(c = -3\).

Step 3 :Calculate the discriminant \(D\) using the formula \(D = b^2 - 4ac\), which gives us \(D = 256\).

Step 4 :Use the quadratic formula \(x = \frac{-b \pm \sqrt{D}}{2a}\) to solve for \(x\).

Step 5 :The solutions to the equation are \(x = 3.0\) and \(x = -0.2\).

Step 6 :So, the final answer is \(\boxed{3.0, -0.2}\).

From Solvely APP
Source: https://solvelyapp.com/problems/8773/

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