Solve the Quadratic Equation: Discover x in 7x^2 + 3x + 8 = 9x + 3

Question

Given the following equation, find its solution

$7x^2+3x+8=9x+3$

00:00 Find X

00:06 Arrange the equation so that the right side equals 0

00:09 Combine like terms

00:18 Identify the coefficients

00:23 Use the quadratic formula to find possible solutions

00:34 Substitute appropriate values and solve to find solutions

00:44 Calculate the square and products

00:52 The root expression is less than 0, therefore no solution exists

To solve the equation $7x^2 + 3x + 8 = 9x + 3$ , follow these steps:

Step 1: Rearrange the equation into standard quadratic form:
Move all terms to one side:
$7x^2 + 3x + 8 - 9x - 3 = 0$ .
Step 2: Simplify the equation:
Combine like terms:
$7x^2 - 6x + 5 = 0$ .
Step 3: Identify coefficients:
$a = 7$ , $b = -6$ , and $c = 5$ .
Step 4: Calculate the discriminant ( $\Delta$ ):
$\Delta = b^2 - 4ac = (-6)^2 - 4(7)(5) = 36 - 140 = -104$ .
Step 5: Determine the nature of the roots:
Since the discriminant is negative ( $\Delta = -104$ ), this means there are no real solutions.

Therefore, the solution to the equation is No solution.

No solution