Final answer:
To solve the equation 5x - 7x² = 3x + 4, use the quadratic formula to find the possible values of x.
Step-by-step explanation:
To solve the equation 5x - 7x² = 3x + 4, we can start by simplifying the equation:
5x - 7x² = 3x + 4
Next, rearrange the equation to get the quadratic equation in standard form:
7x² - 2x - 4 = 0
Now, we can solve the equation either by factoring, completing the square, or using the quadratic formula. In this case, let's solve it using the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / (2a)
Substituting the values from our equation, we get:
x = (-(-2) ± sqrt((-2)² - 4(7)(-4))) / (2(7))
Simplifying further, we have:
x = (2 ± sqrt(4 + 112)) / 14
x = (2 ± sqrt(116)) / 14
Finally, we can simplify the answer:
x = (2 ± 2sqrt(29)) / 14