Question

(420:х)-9=19(х-129):17=12​

Answer 1

Ответ:

Пошаговое объяснение:

(420:х)-9=19

420:х=19+9

420:х=28

Х=420:28

Х=15

(х-129):17=12​

Х-129=12*17

Х-129=204

Х=204+129

Х=333

Answer 2

To solve the equation, we need to find the value of "x" that satisfies the equation (420/x) - 9 = 19(x - 129)/17 = 12. Let's solve it step by step:

Step 1: Simplify the equation (420/x) - 9 = 19(x - 129)/17 = 12

Step 2: Get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. The LCM of x, 17, and 1 is 17x. 17x * [(420/x) - 9] = 17x * [19(x - 129)/17] = 17x * 12

Step 3: Simplify further 17 * 420 - 9x = 19(x - 129) * x = 204x

Step 4: Expand and rearrange the equation 7140 - 9x = 19x^2 - 19 * 129x = 204x

Step 5: Move all the terms to one side of the equation to get a quadratic equation in standard form. 19x^2 - 204x - 9x - 19 * 129 = 0

Step 6: Combine like terms 19x^2 - 213x - 19 * 129 = 0

Now, we have a quadratic equation. We can solve it using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

where a = 19, b = -213, and c = -19 * 129.

Step 7: Substitute the values and calculate "x": x = (213 ± √((-213)^2 - 4 * 19 * (-19 * 129))) / 2 * 19

Step 8: Calculate the discriminant (b^2 - 4ac) to determine the nature of the solutions. Discriminant = (-213)^2 - 4 * 19 * (-19 * 129) = 45369

Since the discriminant is positive, we have two distinct real solutions for "x."

Step 9: Calculate the two values of "x." x = (213 + √45369) / 38 ≈ 21.387 x = (213 - √45369) / 38 ≈ -2.276

So, the solutions for "x" are approximately 21.387 and -2.276.