Solve the Quadratic Equation: Discover x in 7x² + 3x + 8 = 9x + 3

Given the following equation, find its solution

7x2+3x+8=9x+3 7x^2+3x+8=9x+3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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

Step-by-step written solution

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1

Understand the problem

Given the following equation, find its solution

7x2+3x+8=9x+3 7x^2+3x+8=9x+3

2

Step-by-step solution

To solve the equation 7x2+3x+8=9x+3 7x^2 + 3x + 8 = 9x + 3 , follow these steps:

  • Step 1: Rearrange the equation into standard quadratic form:
    Move all terms to one side:
    7x2+3x+8−9x−3=0 7x^2 + 3x + 8 - 9x - 3 = 0 .
  • Step 2: Simplify the equation:
    Combine like terms:
    7x2−6x+5=0 7x^2 - 6x + 5 = 0 .
  • Step 3: Identify coefficients:
    a=7 a = 7 , b=−6 b = -6 , and c=5 c = 5 .
  • Step 4: Calculate the discriminant (Δ \Delta ):
    Δ=b2−4ac=(−6)2−4(7)(5)=36−140=−104 \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 (Δ=−104 \Delta = -104 ), this means there are no real solutions.

Therefore, the solution to the equation is No solution.

3

Final Answer

No solution

Practice Quiz

Test your knowledge with interactive questions

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number


what is the value of \( a \) in the equation

\( y=3x-10+5x^2 \)

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