Х²+4х-21=0

To solve the equation x² + 4x - 21 = 0, we can use the quadratic formula. The quadratic formula states that for any equation in the form of ax² + bx + c = 0, the solutions can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

Applying this formula to our equation, where a = 1, b = 4, and c = -21, we have:

x = (-4 ± √(4² - 4(1)(-21))) / (2(1))

Simplifying further:

x = (-4 ± √(16 + 84)) / 2

x = (-4 ± √100) / 2

x = (-4 ± 10) / 2

This gives us two possible solutions:

x₁ = (-4 + 10) / 2 = 6 / 2 = 3

x₂ = (-4 - 10) / 2 = -14 / 2 = -7

Therefore, the solutions to the equation x² + 4x - 21 = 0 are x = 3 and x = -7.