The solution set of 3x^2=7-4x

x = 1 or x = - 7/3

Step-by-step explanation:

Solve for x over the real numbers:

3 x^2 = 7 - 4 x

Subtract 7 - 4 x from both sides:

3 x^2 + 4 x - 7 = 0

The left hand side factors into a product with two terms:

(x - 1) (3 x + 7) = 0

Split into two equations:

x - 1 = 0 or 3 x + 7 = 0

Add 1 to both sides:

x = 1 or 3 x + 7 = 0

Subtract 7 from both sides:

x = 1 or 3 x = - 7

Divide both sides by 3:

Answer: x = 1 or x = - 7/3